Observer

The observer sees a straight fence 100 m long in 30° view angle. From one end of the fence is 102 m.

How far is it from another end of the fence?

Correct answer:

x =  119.9 m

Step-by-step explanation:

$$\begin{gathered} {\displaystyle \frac{\sin \beta }{\sin 30^{\circ }}}={\displaystyle \frac{102}{60}} \\ \beta =\arcsin ({\displaystyle \frac{102}{60}}\cdot \sin 30^{\circ })=1.016=58\mathrm{°}12^{\mathrm{\prime }}42\mathrm{"} \\ \gamma =180^{\circ }-30^{\circ }-58\mathrm{°}12^{\mathrm{\prime }}42\mathrm{"}=91\mathrm{°}47^{\mathrm{\prime }}18\mathrm{"} \\ {\displaystyle \frac{\sin \gamma }{\sin \beta }}={\displaystyle \frac{x}{102}} \\ x=102\cdot {\displaystyle \frac{\sin \gamma }{\sin \beta }}=119.9\text{ m} \end{gathered}$$

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