Question

Mr. Elliott is heading on a ski trip to Revelstoke Mountain. While driving his car towards the mountain Mr. Elliott measures the angle of elevation to the top of the mountain to be 5°. He drives 15 km closer to the mountairn and measures the new angle of elevation to be 22°. Assuming Mr. Elliott was driving on a level (flat) road, find the height of the mountain (in metres).

Answer 1

Answer on Question #83271 – Math – Trigonometry

Question

Mr. Elliott is heading on a ski trip to Revelstoke Mountain. While driving his car towards the mountain Mr. Elliott measures the angle of elevation to the top of the mountain to be $5{}^{\circ}$. He drives $15\mathrm{km}$ closer to the mountain and measures the new angle of elevation to be $22{}^{\circ}$. Assuming Mr. Elliott was driving on a level (flat) road, find the height of the mountain (in metres).

Solution

Right triangle $\Delta CBO$

$$\tan 5{}^{\circ} = \frac{OC}{OB} = \frac{h}{x + 15}$$

Right triangle $\Delta CAO$

$$\tan 22{}^{\circ} = \frac{OC}{OA} = \frac{h}{x}$$ $$x = \frac{h}{\tan 22{}^{\circ}}$$ $$h = \left(\frac{h}{\tan 22{}^{\circ}} + 15\right) \tan 5{}^{\circ}$$ $$h = \frac{\tan 5{}^{\circ} \tan 22{}^{\circ}}{\tan 22{}^{\circ} - \tan 5{}^{\circ}} \cdot 15 \approx 1.675 \, (\mathrm{km})$$ $$h = 1675 \, \mathrm{m}$$

Answer: The height of the mountain is 1675 metres.

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