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Syllabus

The angle of elevation of a jet plane from a point A on the ground is 60

^{0.}After a flight of 15 sec,the angle of elevation changes to 30^{0}.If the jet plane is flying at a height of 1500 root 3 m,find the speed of the jet plane.A ladder 10m in length touches a wall at height of 5m. The angle made by the ladder with the horizontal is?.. with a diagram

From the top of the building 60m high the angle of depression of the top and bottom of a vertical lamp post are observed to be 30 degree and 60 degree respectively find

a)the distance between the building and the lamp post

b)the height of the lamp post

The height of a tower is 12m .What is the length of its shadow when sun's altitude is 45 degrees?

The angle of elevation of a jet fighter from point A on the ground is 60°.After a flight of 15 seconds, the angle of elevation changes to 30°.If the jet is flying at a speed of 720 km/h, find the constant height at which jet is flying.

A vertical rod is fixed in a horizontal rectangular field ABCD.The angular elevations of its top A ,B,C and D areα ,β,γ andδ

respectively.Show that cot

^{2}α - cot^{2}β= cot^{2}δ- cot^{2}γIf the angle of elevation of a cloud from a point

hmetres above a lake isalphaand the angle of depression of its reflection isbeta. Prove that the height of cloud ish(tan beta + tan alpha)/ tan beta - tan alphaa) 17 m

b) 8 m

c) 10 m

d) 14m

The angle of elevation of a cloud from a point 60m above the lake is 30 and the angle of depression of its reflection in the lake is 60.find the height of the cloud above the lake?

A man standing on the deck of a ship, which is 10m above the water level, observes the angle of elevation of the top of a hill as 60 degree and the angle of depression of the base of the hill as 30 degree. Find the distance of the hill fom the ship and the height of the hill.

^{0}with the horizontal through the foot of the poles . find the length of the wire.The Angle of elevation of th top of a vertical tower from a point on the ground is 60

^{o.}From another point 10m vertically above the first, its angle of elevation is 30^{o.}Find the height of tower? ...................Please provide me answer as soon as possible....A man on a deck of a ship 12m above water level observes the angle of elevation of the top pf a cliff is 60degree and the angle of depression of the base of the cliff is 30degree. Find the distance of the cliff from the ship and the height if the cliff .The angle of elevation of the top Q of a vertical tower PQ from point X on the ground is 60 degree.At a point Y 40m vertically above X the angle of elevation is 45 degree .Find the height Of the tower PQ and distance XQ.

the angles of depression of the top and bottom of an 8m tall building from the top and bottom of a multistoreyed buildin are 30 and 45 degrees respectively. find the height of the multistoreyed building and the distance between the twoo buildings. please anser me fast today is my test.

1)These are two windows in a house.A window of the house is at a height of 1.5m above the ground and the other window is 3mvertically above the lower window.Ram and Shyamare sitting inside the two windows.At an instant,the angle of elevation of a balloon from these windows are observed as 45

^{0 }and 30^{0}respectively.(a)Find the height of the balloon from the ground.

(b) Among Ram and Shyam,who is more closer to the balloon?

(c) Why window are essentialin any construction,commercial or residential?

(d) If the balloon is moving towards the building,then both angles of elevation will remain same or not?

the angles of elevation of the top of a tower from two points at a distance of 4m and 9m from the base of the tower and in the same straight line with it are complementary. prove that the height of the tower is 6 m

evaluate

sin 30^{0}+ tan 45^{0}-cosec 60^{0}sec 30^{0 +}cos 60^{0}+ cot 45^{0}A boy standing on a horizontal plane finds a bird flying at a distance of 100m from

him at an elevation of 30

0. A girl standing on the roof of 20 meter high building finds the angle of elevation of the same bird to be 450. Both the boy and the girl are on opposite sides of the bird. Find the distance of the bird from the girl.

if two towers of height h1 and h2 subtend angles of 60 degree and 30 degree respectively at the midpoint of the line joining their feet , then the ratio of h1: h2

From the top of a hill the angle of depression of the two consecutive kilometre stones due to east are found to be 30

^{o}and 45^{o}.Find the height of a hill.FROM THE TOP OF A TOWER 50M HIGH THE ANGLES OF DEPRESSION OF THE TOP AND THE BOTTOM OF A POLE ARE OBSERVED TO BE 45DEGREE AND 60DEGREE RESPECTIVELY. FIND THE HEIGHT OF THE TOWER

The angle of depression from top of a 12m high at a point on the ground is 30degrees the distance of the point from the top of the tower is

In a flight of 600 km , an aircraft was slowed down due to bad weather. The average speed for the trip was decreased by 200 km/h & the time of flight increased by 30 minutes. Find the duration of flight.

1. a vertical post stands on a horizontal plane. the angle of elevation of the top is 60 ° and that of a point xm be the height of the post, then prove that x=2h/3.

2. a fire in a building B is reported on telephone to 2 fire stations P nd Q, 10 km apart from each other on a straight road.P observes that the fire is at an angle of 60 ° to the road and Q observes that it is angle of 45 ° to the road. which station shold send its team and how much will the team have to travel?

3.a man on a top of tower observes a truck at angle of depressionα where tan α= 1/√5 and sees that it is moving towards the base of the tower. ten minutes later, the angle of depression of the truck is found to be β where tan β= √5, if the truck is moving at a uniform speed, determine how much more time it will take to reach the base of the tower.

a ladder rests against a vertical wall at an inclination of

to the horizontal.its foot is pulled away from the wall through a distancealphapso that its upper end slides a distanceqdown the wall and then the ladder makes an angle ofbetato the horizontal show thatp/q= cos beta - cos alpha/ sin alpha -sin betaA shooter is standing on the ground and is looking at a bird up in the sky, which is at a vertical distance of 11 m. The shooter points the gun towards the bird at an angle of elevation of 30° with the horizontal.

If the shooter is holding the gun at a height of 1 m from the ground, then what is the horizontal distance between the bird and the shooter?

a bird sitting on the top of a tree, which is 80m high. the angle of elevation of the bird, from the point on the ground is 45

^{0}. the bird flies away from the point of observation horizantally and remains at a constant height. after 2 seconds, the angle of elevation of the bird from the point of observation becomes 30^{0}. find the sped of the flying birdgiven the length of a string between a kite and a point on the ground is 93.5 m.If the string makes an angle theta with the level ground such that tan theta is 15 by 8 .Then the height of the kite is????

From a top of a 7m high building, the angle of elevation of the top of a cable tower is 60 degree & the angle of depression of its foot is 45 degree. Determine the height of the tower.

PLZ ANSWER IN UNDERROOTS & WITH THE FIGURE.

as observed from the top of a lighthouse 100m above sea level the angle of depression of a ship sailing directly towards it changes from 30 degree to 60 degree. determine the distance travelled by the ship during the period of observation

a pole 6 m high casts a shadow 2 root 3 m on the ground then the sun's elevation is :

a-60 degrees

b-45 degrees

c - 30 degrees

d-90 degrees

An aeroplane flying horizontally 1 km above the ground is observed at an elevation of 60V. After a flight of 10 seconds, its angle of elevation is observed to be 30V from the same point on the ground. Find the speed of the aeroplane in km/hour.

Q. Evaluate : $\frac{3\mathrm{sin}3A+2\mathrm{cos}\left(5A+10\xb0\right)}{\sqrt{3}\mathrm{tan}3A-\mathrm{cos}ec\left(5A-20\xb0\right)}$, when A = 10$\xb0$.

At the foot of a mountain the elevation of its summit is 45° . After ascending 1000m

^{0}, find the length of its shadow.16)the angle of elevation of the top of a tower from a point A on the ground is 30 degree.on moving a distance of 20metres towards the foot of the tower to a point B the angle of elevation increases to 60 degree.find the height o the tower and the distance of the tower from the point A.

A bridge, in the shape of straight path, across a river, makes an angle of 60 with the width of

the river. If the length of the bridge is 100 metres, then the width of the river is

(A) 50 m (B) 173.2 m (C) 43.3 m (D) 100 m

A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car as an angle of depression of 30°, which is approaching the foot of the tower with a uniform speed. Six seconds later, the angle of depression of the car is found to be 60°. Find the time taken by the car to reach the foot of the tower from this point.

The length of the shadow of a tower standing on level ground is found to be 2x metres longer

when the sun’s altitude is 30° than when it was 45°. Prove that the height of tower is (√3+1)x

metres.

Find the distance of the point from the top of the tower .

Experts answer fast

A fire in building B is reported on telephone to two fire stations P and Q, 20 km apart from each other on a straight road. P observes that the fire is at an angle of 60 degree to the road and Q observes it an angle of 45 degrees to the road.Which station should send its team and how much will the team have to travel ?

if root 3 tan theta=1, then find the value of sin

^{2}theta-cos^{2}thetaan aeroplane at an altitude of 200m the angle of depression of two opposite pointso two banks of a river to be 45 and 60 degrees. find the width of the river in meters

From a point on the ground, the angles of elevation of the bottom and the top of a transmission tower fixed at the top of a 20 m high building are 45° and 60° respectively. Find the height of the tower

A fire in the building B is reported on telephone to two fire stations P and Q, 20km apart from each other on a straight road. P observes that the fire is at the angle of 60° to the road and Q observes that it is at an angle of 45° to the road. Which station should send its team and how much will this team have to travel?

if

costheta +costheta =^{2}1than prove thhatsintheta +^{2}sintheta=^{4}1Two poles of equal heights are standing opposite each other on either side of the road, which is 80 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 60 digree and 30 digree, respectively. Find the height of the poles and the distance of the point from the poles.

9) a vertical tower stands on a horizontal plane and is surmounted by a vertical flag-staff of height 5 metres.at a point on the plane,the angles of elevation of the bottom and the top of the flag-staff are respectively 30 degree and 60 degree.find the height of the tower.

the tops of two poles of height 16m and 10m are connected by a wire . If the wire makes an angle of 30 with the horizontal , then the length of the wire ... ??From a point 100m above a lake the angle of elevation of a 30 degree and angle of depression of its reflecting in the lake is 60 degree. find the height of helicopter.

the height of a tower is half the height of the flagstaff on it. the angle of elevation of the top of the tower as seen from a point on the ground is 30.find the angle of elevationof the top of the flagstaff as seen from the same point ?

The ratio of the length of a tree and its shadow is 1:1/.The angle of sun's elevation is

Two boats approach a light house in mid-sea from opposite directions.The Angles of elevation of the top of the light house from two boats are 60 and 45 respectively.If the distance between the two boats is 100m,find the height of hte light house.

the length of a string between a kite and a point on the ground is 90 m. If the string makes an angle Θ with the ground level such that tan Θ = 15/8 , how high is the kite ? Assume there is no slack in the string .

ans 79.41m

A tree 12m high, is broken by the wind in such a way that its top touches the ground and makes an angle of 60degree with the ground .. At what height from the bottom, the is broken by the wind???An aeroplane flying horizontally 1000m above the ground is observed at an angle of elevation 60

^{0}froma point on the ground.Aftera flight of 10secondsthe angle of elevation at a point of observation changes to 30^{0}.Find the speed of the plane in m/s.angle of elevation of the top of the hill at the foot of tower is 60 degrees and the angle of elevation of tower from the foot of the hill is 30 degrees. if tower is 50m high find the height of hill

A man on cliff observes a boat at an angle of depression of 30 degree which is approaching the shore to the point immediately beneath the observer with a uniform speed. Six minutes later , the angle of depression of the boat is found to be 60 degree . Find the total time taken by the boat to reach the shore .

A 1.6m tall, girl stands ata distance of 3.2m from a lamp-post and cats a shadow of 4.8m on the grond. Find the height of the lamp-post by using (i)trignometric ratios (ii)property of similiar triangles.

A round balloon of radius r subtends an angle α at the eye of the

the angles of depression of two ships from the top of a light house are 45 and 30 towards east.if the ship some 100 m apart find the height of light house?

The angle of elevation of the top of a tower as observed from a point on the ground is

αand on moving 'a' metre towards the tower the angle of elevation isβ.Prove that the height of the tower isa tanα.tanβtan

β- tanαAt a point on level ground, the angle of elevation of a vertical tower is found such that it's tangent is 5/12 . On walking 19.2 mtrs towards the tower , the tangent of the angle of elevation is 3/4 . Find height of the tower?????

A peacock is sitting on the top of a tree. It observes a serpent on the ground making an angle of depression of 30degree .The peacock with the speed of 300m/minute catches the serpent in 12seconds. What is the height of the tree?

As observed from the top of a 75 m high lighthouse from the sea-level, the angles of depression of two ships are 30° and 45°. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships.

a man standing on the top of a multi-storey building, which is 30m high, observes the angle of elevation of the top of a tower as 60 degrees and the angle of depression of the base of the tower as 30 degrees. Find the horizontal distance between the building and the tower. also find the height of the tower.

An aeroplane flying horizontally at a height of 2500m above the ground is observed at a certain point on earth to subtend and angle of 60

^{0}. After 15 seconds, its angle of elevation at the same point is observed to be 30^{0}. Calculate the speed of the aeroplane.attached to her telescope, she fi nds the angle of depression to the bottom of this tree is 30?, while the angle of elevation to the

top of the tree is 60?. The angle of elevation to the troop of baboons is 45?. Use this information to fi nd (a) the height of the

observation post, (b) the height of the baboons? tree, and (c) the height of the baboons above ground.

The shadow of a tower standing on the level ground is found to be 40 m

longer when the sun’s altitude is 30 than when it is 60Find the height

of the tower.

Q.There are two temples, one on each bank of a river, just opposite to each other. One temple is 50m high. From the top of this temple, the angles of depression of the top &the foot of the other temple are 30^{0}& 60^{0}respectively. Find the width of the river and the hight of the other temple.the angle of elevation of an aeroplane from a point on the ground is 45 degree. After 15 seconds of flight the angle changes to 30 degree.f the plane is flying at a constant height of 2500m,find the speed of the plane.

A man on the roof of a house,which is 10m high observes the angle of elevation of the top of a building as 60

^{o}and the angle of depression of the base of the building as 45^{o}.Find the height of the building and its distance from the house.FAAST GUYZ!! MA ASSIGNMENT

IF A PERSON ONWALKING 20 M TOWARDS CHIMNEY IN A HORIZONTAL LINE THROUGH ITS BASE OBSERVES THAT ITS ANGLE OF ELEVATION CHANGES FRO 30 TO 456 THEN THE HEIGHT OF CHIMNEY???

A vertical stick 20cm long casts a shadow 15cm long. At the same time, a tower casts a shadow 30 metre long. What is the height of the tower ?

A tree breaks due to storm and the broken part bends, so that the top of the tree touches the ground making an angle of 30 degree with the ground. The distance between the foot of the tree to the point where the top touches the ground is 8m find he height of the tree.

a balloon is connected to an electric pole by a cable of length 215m inclined at 60 degree to the horizontal. determine the height of the balloon from the ground . also , find the height of the balloon if the angle of inclination is changed from 60 degree to 30 degree.

a man standing on deck of ship which is 10m above the sea level, observes the angle of elevation of the top of a cloud as 30 degree and angle of depression of its reflection in the sea was found to be 60 degree. find the height of the cloud and also the distance of cloud from the ship