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=(Perpendicular)/(Base)`

`\\ \rm\rightarrowtail tan20=(x)/(10)`

`\\ \rm\rightarrowtail 0.364=(x)/(10)`

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

`\\ \rm\rightarrowtail x=3.64mi`

Answer 2

`\displaystyle 4\:mi.`

Explanation:

`\displaystyle (10)/(h) = cot\:20 \hookrightarrow 10 = hcot\:20 \hookrightarrow (10)/(cot\:20) = h; 3,6397023427... \\ \\ \boxed{4 \approx h}`

OR

`\displaystyle (h)/(10) = tan\:20 \hookrightarrow 10tan\:20 = h; 3,6397023427... \\ \\ \boxed{4 \approx h}`

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