VALUE BASED QUESTION:- AHIGHWAY LEADS TO THE FOOT OF 300m HIGH TOWER AN OBSERVATORY IS SET AT THE TOP - Maths - Some Applications of Trigonometry

Question

VALUE BASED QUESTION:-
AHIGHWAY LEADS TO THE FOOT OF 300m HIGH TOWER AN
OBSERVATORY IS SET AT THE TOP OF THE TOWER IT SEES A CAR MOVING
TOWARDS IT AT AN ANGLE OF DEPRESSION OF 30 DEGREE AFTER 15 SECONDS
ANGLE OF DEPRESSION BECOMES 60 DEGREE

A) FIND THE DISTANCE TRAVELLED BY THE CAR DURING THIS TIME
B) HOW THIS OBSERVATORY IS HELPFUL TO REGULATE THE TRAFFIC ON THE
HIGHWAY

Manbar Singh · Accepted Answer

Let AB be the tower
 Now, AB = 300 mLet D be the first poisition and C be the second position of the car
Let ∠ADB = 30°; ∠ACB = 60°In ∆ABC,tan 60° = ABBC⇒3 = 300BC⇒BC = 3003 = 30033 = 1003 mIn ∆ABD,tan 30° = ABBD⇒13 = 300BC + CD⇒BC + CD = 3003⇒1003 + CD = 3003⇒CD = 2003 mSo, distance between 2 positions = 2003 = 200 × 1
73 = 346 mSo, distance travelled in 15 sec = 346 m