Question

From a balloon rising vertically a boy observes two consecutive kilometer-stones on the same side of
a straight road and find their angles of depression as 45° and 30°; find the altitude of the balloon.

Answer 1

Answer:

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10th

Maths

Some Applications of Trigonometry

Heights and Distances

From the top of a hill, the...

MATHS

From the top of a hill, the angles of depression of two consecutive kilometer stones due east are found to be 30o and 45o. Find the height of the hill

A

1.365km

B

1.5km

C

1.7km

D

1.1km

HARD

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ANSWER

Let the distance between the nearer kilometre stone and the hill be 'x' km. 

So, the distance between the farther kilometre stone and the hill is '1+x' km since both are on the same side of the hill.

In triangle APB,

 tan450=xh

       ⇒1=xh

       ⇒h=x

In triangle AQB,

 tan300=1+xh

 ⇒31=1+xh

⇒1+x=3h

From equation 1,

1+h=3h⇒1=3h−h

⇒h=

Answer 2

answer is √3+1/2

hope this help you