Question

The height of the hill is 340 m. As observed from the top of the hill, the angle of depression of

two houses situated at East and west side of the hill is found to be 30° and 60° respectively. Find

the distance between the two houses​

Answer 1

Answer:

1.365km

Step-by-step explanation:

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=3−11 

⇒h=1.365km

Hope this help you.

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