Height of the pole

Geometry Level 3

The top of a 15 metre high tower makes an angle of elevation of 60º with the bottom of an electric pole and angle of elevation of 30º with the top of the pole. What is the height of the electric pole?(in metres)


The answer is 10.

Anuj Shikarkhane by Anuj Shikarkhane , 19, India

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1 solution

By law of sines,

h sin ⁡ 30 = x sin ⁡ 120 \dfrac{h}{\sin~30}=\dfrac{x}{\sin~120} ⟹ \implies h = sin ⁡ 30 sin ⁡ 120 x h=\dfrac{\sin~30}{\sin~120}x

However, sin ⁡ 60 = 15 x \sin~60=\dfrac{15}{x} , from here, x = 15 sin ⁡ 60 x=\dfrac{15}{\sin~60}

So

h = sin ⁡ 30 sin ⁡ 120 ( 15 sin ⁡ 60 ) = h=\dfrac{\sin~30}{\sin~120}\left(\dfrac{15}{\sin~60}\right)= 10 \boxed{10}

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