First slide

Applications of trigonometry

Question

If a flag-staff of 6 meters height placed on the top of a tower throws a shadow of 2 $\sqrt{3}$ meters along the ground then the angle (in degrees) that the sun makes with the ground is

Moderate

A

$60^{0}$
B

$30^{0}$
C

$45^{0}$
D

$75^{0}$

Solution

Let OA and AB be the shadows of tower OP and flag staff PQ respectively on the ground. Suppose the sun makes an angle $θ$ with the ground.
Let $O A = x$ . In triangles OAP and OBQ, we have $\tan θ = \frac{h}{x}$ and $\tan θ = \frac{h + 6}{x + 2 \sqrt{3}}$
$∴ \frac{h}{x} = \frac{h + 6}{x + 2 \sqrt{3}}$
$h x + 2 \sqrt{3} h = h x + 6 x$
$\Rightarrow 2 \sqrt{3} h = 6 x \Rightarrow x = \frac{h}{\sqrt{3}}$
$∴ \tan θ = \frac{h}{x} \Rightarrow \tan θ = \sqrt{3} \Rightarrow θ = 60^{0}$

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