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Unformatted text preview: nearest foot?
1. We can represent the problem situation using a right triangle as shown below. If we let h
denote the height of the tower, then Theorem 10.10 gives tan (60◦ ) = 30 . From this we get
h = 30 tan (60◦ ) = 30 3 ≈ 51.96. Hence, the Clocktower is approximately 52 feet tall. h ft. 60◦
Finding the height of the Clocktower
2. Sketching the problem situation below, we ﬁnd ourselves with two unknowns: the height h of
the tree and the distance x from the base of the tree to the ﬁrst observation point. h ft.
30◦ 45◦ 200 ft. x ft. Finding the height of a California Redwood
6 Named in honor of Raymond Q. Armington, Lakeland’s Clocktower has been a part of campus since 1972. 646 Foundations of Trigonometry
Using Theorem 10.10, we get a pair of equations: tan (45◦ ) = h and tan (30◦ ) = x+200 . Since
tan (45◦ ) = 1, the ﬁrst equation gives x = 1, or x = h. Substituting this into the second
equation gives h+200 = tan (30◦ ) = 33 . Clearing fractio...
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