Question

From the top of a hill, the angles of depression of two consecutive kilometre stones due east are found to be 30°and 45°. Find the distance of the two stones from the foot of the hill. ​

Answer 1

Answer:

Hence, the height of the hill is 1.365 km.

Answer 2

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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

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