## anonymous 4 years ago From a hot-air balloon 2 km high, the angles of depression to two towns, in line with the balloon, are 81.2 degrees and 13.5 degrees. How far apart are the towns?

1. anonymous

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2. anonymous

k, simple trigonometric relations here, we know that in a right angle triangle the tan of one of the angles is equal to the opposite side over the adjacent side: $\tan \theta = \frac{opposite}{adjacent}$for your case, you simply need to rearrange that equatiion to find the length of the bottom side for each angle. $\text{ie } D_1 = \frac{2}{\tan(81.2)} \space D_2 = \frac{2}{\tan(13.5)}$ then find the difference between D1 and D2

3. anonymous

Wow.. I was thinking too hard haha.. its too easy. thanks!!!

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