SOLUTION: A tree has grown at one corner of a school yard 35m long and 55 wide. The angle of elevation of the top of the tree from the opposite corner of the school yard is 17 degrees. Calcu

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Question 1149060: A tree has grown at one corner of a school yard 35m long and 55 wide. The angle of elevation of the top of the tree from the opposite corner of the school yard is 17 degrees. Calculate the height of the tree and the angle of elevation from the other two corners of the courtyard.
Answer by greenestamps(13209) About Me  (Show Source):
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The diagonal of the yard can be found using the Pythagorean Theorem.

sqrt%2855%5E2%2B35%5E2%29+=+65.192 to 3 decimal places.

In the right triangle with the 17 degree angle of elevation to the top of the tree, the height of the tree is the side opposite the 17 degree angle and the diagonal of the yard is the side adjacent to that angle. So the trig function is tangent.

tan%2817%29+=+h%2F65.192
h+=+65.192%2Atan%2817%29+=+19.93 to 2 decimal places

From one of the other two corners of the yard, the tangent of the angle of elevation is 19.93/55; from the other corner it is 19.93/35.

tan%28x%29+=+19.93%2F55
x+=+arctan%2819.93%2F55%29

And similarly

tan%28x%29+=+19.93%2F35
x+=+arctan%2819.93%2F35%29

Use a calculator....