Class 10

Math

All topics

Some Applications of Trigonometry

A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car at an angle of depression of $30_{o}$, 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 $60_{o}$. Find the time taken by the car to reach the foot of the tower from this point.

$tan30=ACCO =dx =3 $ ....(1)

$tan60=3 =BCDC =yx $ ...(2)

from (1) and (2)

$d=3 x=3 (3 y)=3y$

$∴speed=timedistance $

from A to B

speed $=6d−y $

required

time $=speeddistance (from B to c) $

$=6d−y y $

$=d−y6y $ $(∵d−3y)$

$=3y−y6y $

$=2y6y $

$=3$ sec