Heights and Distances Practice Test 2

Question : 20 of 24

Marks: +1, -0

A radio transmitter antenna of height 100 mstands at the top of a tall building. At a pointon the ground, the angle of elevation ofbottom of the antenna is 45° and that of thetop of the antenna is 60°. What is the heightof the building?

100 m
50 m
$50(√ 3+1 )$ m
$50(√ 3-1 )$ m
None of these

Validate

Solution:

Let BC be a building of height h metre and CD = 100 m be the height of the antenna.

In ΔABC,

\tan 45 °=h/x⇒x=h

In ΔABC,

\tan 60°={100+h}/x

⇒√ 3={100+h}/h

⇒h=100/{(√ 3-1 )}×(√ 3+1 )/(√ 3+1 )

=50(√ 3+1 )m

Go to Question:

Prev Question

Next Question