Choose the one alternative that best completes the statement or answers the question.
-A flagpole is perpendicular to the horizontal but is on a slope that rises 10° from the horizontal. The pole casts a 43-foot shadow down the slope and angle of elevation of the sun measured from the slope is 36°. How tall is the
Pole? Round your answer to the nearest 0.1 foot.
A) 33.5 ft
B) 36.4 ft
C) 35.4 ft
D) 36.2 ft

Question

Quizplus · Accepted Answer

To find the height of the pole, we can use trigonometry, specifically the tangent function, which relates the angle of elevation to the ratio of the opposite side (height of the pole) over the adjacent side (length of the shadow). The angle of elevation of the sun relative to the horizontal is 36° + 10° = 46° because the slope itself is at a 10° incline from the horizontal, and the sun's elevation is measured from the slope. Using the tangent function: tan(46°) = height / 43 feet. Solving for height gives us height = 43 * tan(46°), which approximately equals 36.4 feet when rounded to the nearest 0.1 foot.

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