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# You want to measure the height of a tree growing vertically on the side of a hill.  The hill makes an angle of 20°with the horizontal.  Standing 15ft. downhill from the base of the tree, you measure the angle formed by the hill and the top of the tree to be 45°.  Find the height of the tree to the nearest foot.  Show your work.

By drawing a diagram that represents the problem, obtain triangle ABC such that m∠A = 45° AB = 15 ft, distance downhill Let BC = h, the vertical height of the tree. Because AB is 20° above the horizontal, m∠C = 90 -(20+45) = 25°. Apply the Law of Sines to obtain $\frac{h}{sin45} = \frac{15}{sin25}$ $h=15(\frac{sin45}{sin25} )=25.1$ Answer: 25 ft (nearest foot)