Question

pls solve that question​

Answer 1

Hello there,

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k...

height if boy      = 1.7m (#not  so important)

height of tower = 30m

and given relation

$sin(\alpha +\beta)=cos(\beta - \alpha)=\frac{\sqrt{3}}{2}$

solving this relation by taking arc' sine and arc' cosine (i.e; the inverse trig relation).

we get two equations

$\alpha + \beta =\frac{\pi}{3}\\\\and \\\beta-\alpha=\frac{\pi}{6}$

solving these equations:

we get the values of $\alpha\ and\ \beta$

$\alpha = \frac{\pi}{12}\\\\and \\\\\beta=\frac{\pi}{4}$

using these angles of inclination, and the height of the tower we can find the distances of the boy from the tower at both positions...

$tan(\alpha)=\frac{30}{d_{1} }\\\\tan(\beta)=\frac{30}{d_{2} }\\\\substituting\ \alpha\ and\ \beta$

we get,

$d_{1} =60+30\sqrt30\\\\and\\\\d_{2}=30$

so distance traveled by the boy will be the difference of these two values

i.e

[distance= 30 +√30 m]

which is independent of his height because angle of inclination is in the perspective of the boy.

Cheers.

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