anonymous
  • anonymous
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?
Mathematics
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anonymous
  • anonymous
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?
Mathematics
jamiebookeater
  • jamiebookeater
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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

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