Shadow Golf
Shadow Golf
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I need some word problem help please!?
How can I solve these step by step??
A man 5 ft 8 in. tall stands on a sidewalk that slopes down at a constant angle. A vertical street lamp directly behind him causes his shadow to be 22 ft long. The angle of depression from the top of the man to the tip of his shadow is 31°. If the man is 15 ft down the sidewalk from the street lamp, find the height of the light above the sidewalk. (Round your answer to two decimal places.)
The distance from the tee to the green of a particular golf hole is 340 yd. A golfer hits his drive and paces its distance off at 150 yd. From the point where the ball lies, he measures an angle of 160° between the tee and the green. Find the angle of his drive off the tee measured from the dashed line from the tee to the green shown in the figure. (Round your answer to two decimal places.)
➊ "A man 5'8" tall ..." ➞ "A man 5⅔ feet tall ..."
see my sketch at: http://sogacity.com/images/manonsidew.png
The angle that the sidewalk slopes down (no info given anyway), and "the 31º angle of depression...", is not required to solve the problem.
What we DO have is two similar ∆'s, namely ∆ABC, and ∆ADE, and similar figures have the property that pairs of corresponding sides are in the same ratio.
∴ x : 5⅔ = (15 + 22) : 22 ➞ x : 5⅔ = 37 : 22
∴ x = 37(5⅔) ÷ 22 = 9.53 (to 2 dec.places)
The height of the lamp above the sidewalk is 9.53 feet.
➋ see my drawing at: http://sogacity.com/images/golfersdri.png
We can use the Law of Sines for this question.
We have ∆TBF, and the sine law says that: t : sin T = b : sine B = f : sine F
where f = 150, b = 340, and ∠B = 160º
b : sine B = f : sine F ➞ 340 : sin160 = 150 : sinF
∠F = sin⁻¹[150(sin160) ÷ 340] = 8.6785 ... = 8.68º (2 dec.pl.)
∴ ∠T = 180 – 160 – 8.68 = 11.32º
∴ the angle of his drive off the tee measured from the line from the tee to the flag is 11.32º
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