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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.if

costheta +costheta =^{2}1than prove thhatsintheta +^{2}sintheta=^{4}1From 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

Find the cosine of the angle swept by the minute hand of a clock in 20 minutes.

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.

If 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 alphaThe 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.

if cosec A - cot A =13 then find the value of (cosec A + cot A)

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....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.

^{0}with the horizontal through the foot of the poles . find the length of the wire.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.

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

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.

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

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

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.

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$\xb0$.

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 betacos

^{2}~~0~~/(1-tan~~0~~) + sin^{3}~~0~~/(sin~~0~~- cos~~0~~) = (1+sin~~0~~cos~~0)~~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 birdFrom 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

observed that the angle of elevation of the top of the

tower changed to 60

^{0}from 45^{0}. How much more thanwill he take to reach of the tower?

(a) 5 min

(c) $5\left(\sqrt{3}-1\right)$min

(b) 5$\sqrt{3}$ min

(d) None of these

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

WITHOUT USING TRIGONOMETRIC TABLE,PROVE-

sin 5 tan 22 sec 60 tan 68 sec 85 = 2

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.

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 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.

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 ?

1. an aeroplane flying horizontally at a height of 1.4km above the ground is observed at an elevation od 60degree. after 15 s , its elevation at the same point is obsreved to be 30degree. calculate the speed of the aeroplane in km/h.

2. the angle of elevation of a jet fighter from point A on the ground is 60degree. after a flight of 15 sec, the angle of elevation changes to 30degree. if the jet is flying at a speed of 720km/h, find the constant height at which the jet is flying. (root3=1.732)

3. at a point on the ground level, the angle of elevation of the vertical tower is found to be such that its tangent is 5/12. on walking 240m towards the tower, the tangent of the angle of elevation becomes 3/4. find the height of the tower.

3.the angles od depressio of the top an dbottom of 8m tall building from the top of a multistorey building are 30 and 45 degrees respectyively. find the height of the multi-storey bldg and the distance b/w the 2 bldgs.

4. from the top of a hill. the angles of depression of 2 consecutive km stones due east are found to be 30 and 45 respectively . find the height of the hill.

5. a bird sitting on the top of a tree, which is 80m high.the angle of elevation of the bird from a point on the ground is 45. the bird flies away from the point of observation horizontally and remains at a constant height. after 2 sec, the angle of elevation of the bird from the point of observation becomes30. find the speed of the bird.

6. the angles of elevation of the top of a tower as seen from 2 points A and B situated in the same line and at distances p and q respectively from the foot of the tower are complementary. prove that the height of the tower is rootpq.

7.from a window(60m above the ground) of a house in the stret, the angle of elevation and depression of the foot of the house on the opposite side of the street rae 60 and 45 respectively, show that the height of the opposite house is 60(i = root3).

an 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

How many times will the wheel of a car rotate in a journey of 2002 m, if the radius of the wheel is 49 cm?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?

a girl of height 90cm is walking away from the base of a lamp post at a speed of 1.2m/s if the lamps is 3.6 m above the ground, find

Two 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.

SinQ/(SecQ+tanQ-1) + CosQ/(CosecQ+CotQ-1)=1

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.

A bridge across a river makes an angle of 30 with the river bank. If the length of the bridge across the river bank is 90m what is the width of the river.

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.

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 .Sin

^{4 }+ Cos^{4}= 1 - 2Sin^{2}Cos^{2}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.

how do we find the roots

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???If 5 tan

^{2 }θ -5 tanθ -1 =0, then find the value of 5 tanθ - cotθangle 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 straight highway leads to the foot of a tower .A man standing at the top of the tower

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?

At 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?????

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.

The boy whose eye level is 1.3m from the ground, spots a balloon moving with the wind in a horizontal line at some height from the ground. The angle of elevation of the balloon from the eyes of the boy at an instant is 60

^{0}. After 2 seconds, the angle of elevation reduces to 30^{0}. If the speed of the wind is 29√3m/s,then find the height of the balloon from the ground.Hint : Distance covered by the balloon in 2sec = 29√3 x 2 = 58√3m

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.AT A POINT ON A LEVEL GROUND THE ANGLE OF ELEVATION OF A TOWER IS FOUND TO BE SUCH THAT ITS TANGENT IS 5/12 . ON WALKING 192 TOWARD THE TOWER THE TANGENT OF ITS ANGLE FOUND TO BE 3/4 . FIND THE HEIGHT OF TOWER?

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.

if cosec theta -sin theta = a cube and sec theta -cos theta = b cube then prove that a square.b sq(a sq + b sq) = 1

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 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

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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 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.

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 man notices two objects in a straight line due west. after walking a distance c due north he observes that the objects subtend an angle A at his eye; and after walking a further distance 2c due north they subtend an angle B . if height of the man is being neglected then prove that the distance between the objects is

8c / 3cotB - cotA

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