Question

A boy sees a bird sitting on a tree at an angle of elevation of 20°. If a boy is standing 10 miles away from the tree, at what height bird is sitting? ​

Answer 1

Let that be x

$\\ \rm\rightarrowtail tan\theta=\dfrac{Perpendicular}{Base}$

$\\ \rm\rightarrowtail tan20=\dfrac{x}{10}$

$\\ \rm\rightarrowtail 0.364=\dfrac{x}{10}$

$\\ \rm\rightarrowtail x=10(0.364)$

$\\ \rm\rightarrowtail x=3.64mi$

Answer 2

Answer:

$\displaystyle 4\:mi.$

Step-by-step explanation:

$\displaystyle \frac{10}{h} = cot\:20 \hookrightarrow 10 = hcot\:20 \hookrightarrow \frac{10}{cot\:20} = h; 3,6397023427... \\ \\ \boxed{4 \approx h}$

OR

$\displaystyle \frac{h}{10} = tan\:20 \hookrightarrow 10tan\:20 = h; 3,6397023427... \\ \\ \boxed{4 \approx h}$

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