Question

A flagpole 25 ft high, standing on the edge of the roof of a high building, when seen from a point A on the ground subtends an angle of 3°50’. If A is 200 ft from the bottom of the pole, how far is it from the top?

Answer 1

Answer on Question #77730 – Math – Trigonometry

Question

A flagpole 25 ft high, standing on the edge of the roof of a high building, when seen from a point A on the ground subtends an angle of $3{}^{\circ}50'$. If A is 200 ft from the bottom of the pole, how far is it from the top?

Solution

Given:

$$\begin{array}{l} a = 25 \, ft, \\ b = 200 \, ft, \\ \alpha = 3{}^{\circ}50' = 3.833{}^{\circ}, \\ c = ? \end{array}$$

The equation for the angle $\beta$ can be implied from the law of sines:

$$\sin \beta = \frac{b}{a} \sin \alpha$$ $$\sin \beta = \frac{200}{25} \sin 3{}^{\circ}50' = 0.5348$$ $$\beta = \sin^{-1} 0.5348 = 32.33{}^{\circ}$$

The third angle is

$$\gamma = 180{}^{\circ} - \alpha - \beta = 180{}^{\circ} - 3.833{}^{\circ} - 32.33{}^{\circ} = 143.837{}^{\circ}$$

The third side can then be found from the law of sines:

$$c = a \frac{\sin \gamma}{\sin \alpha} = 25 \cdot \frac{\sin 143.837{}^{\circ}}{\sin 3.833{}^{\circ}} = 220.7 \, ft$$

Answer: 220.7 ft

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