53 using a 2 to see what these dierences are and then

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Unformatted text preview: nearest foot? Solution. 1. We can represent the problem situation using a right triangle as shown below. If we let h 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◦ 30 ft. 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 h Using Theorem 10.10, we get a pair of equations: tan (45◦ ) = h and tan (30◦ ) = x+200 . Since x h tan (45◦ ) = 1, the first equation gives x = 1, or x = h. Substituting this into the second √ √ h equation gives h+200 = tan (30◦ ) = 33 . Clearing fractio...
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This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

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