The angle of elevation of the top of a hill at the foot of a tower is 60⁰ and the angle of depression from the top of the tower of the foot of the hill is 30⁰. If the tower is 50 m high, find the height of the hill.

Solution

Let the height of hill is h.

In right triangle ABC,

$\frac{50}{AB} = \tan 30^{0} \Rightarrow \frac{50}{AB} = \frac{1}{\sqrt{3}} \Rightarrow AB = 50 \sqrt{3} In right triangle ABD, \frac{h}{AB} = \tan 60^{0} \Rightarrow \frac{h}{AB} = \sqrt{3} \Rightarrow h = \sqrt{3} AB \Rightarrow h = \sqrt{3} (50 \sqrt{3}) = 150 m .$

Hence the height of hill is 150 m.

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Some Applications Of Trigonometry

The angle of elevation of the top of a hill at the foot of a tower is 60⁰ and the angle of depression from the top of the tower of the foot of the hill is 30⁰. If the tower is 50 m high, find the height of the hill.

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For Daily Free Study Material Join wiredfaculty

Some Applications Of Trigonometry

The angle of elevation of the top of a hill at the foot of a tower is 600 and the angle of depression from the top of the tower of the foot of the hill is 300. If the tower is 50 m high, find the height of the hill.

Some More Questions From Some Applications of Trigonometry Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

The angle of elevation of the top of a hill at the foot of a tower is 60⁰ and the angle of depression from the top of the tower of the foot of the hill is 30⁰. If the tower is 50 m high, find the height of the hill.