A flagpole

A flagpole is leaning at an angle of 107° with the ground. A string fastened to the top of the flagpole is holding up the pole. The string makes an angle of 38° with the ground, and the flagpole is 8 m long. What is the length of the string?

Correct answer:

s =  12.4264 m

Step-by-step explanation:

$$\begin{gathered} f=8\text{m} \\ \alpha =107{}^{\circ } \\ \beta =38{}^{\circ } \\ \gamma =180-\alpha =180-107=73{}^{\circ } \\ \sin \gamma =h:f \\ h=f\cdot \sin \gamma =f\cdot \sin 73°=8\cdot \sin 73°=8\cdot 0.956305=7.65044\text{m} \\ \sin \beta =h:s \\ s=h/\sin \beta =h/\sin 38°=7.6504/\sin 38°=7.6504/0.615661=12.426=12.4264\text{m} \end{gathered}$$

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