The angle of elevation of the top of a tower as observed from a point in a horizontal plane through the foot of the tower is $32 ° .$ When the observer moves towards the tower at a distance of100 $m$ , he finds the angle of elevation of the top to be $63 °$ , then find the distance between the tower and the first position.

see full answer

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

146.7 m

145.7 m

143.7 m

149.7 m

answer is A.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

Given,
Angle of elevation of top of a tower is

32 ° .

Consider the figure,
Question Image

Let ‘h’ be the height of tower,

tan 63 ° = height of the tower base of the tower ⇒ tan 63 ° = h x ⇒ h = x tan 63 °

Similarly,

tan 32 ° = height of the tower distance of observer from tower ⇒ tan 32 ° = h x + 100 ⇒ h = (x + 100) tan 32 °

Comparing the heights,

x tan 63 ° = (x + 100) tan 32 ° ⇒ 19626 x = 0.6248 x + 62.48 ⇒ 13378 x = 62.48 ⇒ x = 46.7

The distance between the tower and first position,

d = x + 100 ⇒ d = 46.7 + 100 ⇒ d = 146.7 m

Therefore, the distance between the tower and first position is 146.7 m.
Hence, option 1 is correct.

Watch 3-min video & get full concept clarity