SOLUTION: What is the perimeter of a 45°-45°-90° triangle with a hypotenuse length of 28 feet? (Please round to the nearest whole number.)

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Question 316537: What is the perimeter of a 45°-45°-90° triangle with a hypotenuse length of 28 feet? (Please round to the nearest whole number.)

Found 2 solutions by Fombitz, CharlesG2:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Use the Pythagorean theorem to find the side length, s.
s%5E2%2Bs%5E2=28%5E2
s%5E2=28%5E2%2F2
s=28%2A%28sqrt%282%29%2F2%29=14sqrt%282%29
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P=28%2B2s
highlight%28P=28%2B28sqrt%282%29%29

Answer by CharlesG2(834) About Me  (Show Source):
You can put this solution on YOUR website!
What is the perimeter of a 45°-45°-90° triangle with a hypotenuse length of 28 feet? (Please round to the nearest whole number.)
tan 45 = opposite/adjacent = 1
cos 45 = adjacent/hypotenuse = 1/hyp
sin 45 = opposite/hypotenuse = 1/hyp
hyp * sin 45 = 1
hyp = 1/(sin 45) = 1/(sqrt(2)/2) = 1/1 * 2/(sqrt(2) = 2/sqrt(2)
hyp = 1/(sin 45) = 2/sqrt(2) * sqrt(2)/sqrt(2) = 2sqrt(2)/2 = sqrt(2)
cos 45 = adjacent/hypotenuse = 1/hyp
45-45-90 triangles are in the ratio 1-1-sqrt(2)
so each side is the hypotenuse/sqrt(2)
side length = 28/sqrt(2) = 28sqrt(2)/2 = 14sqrt(2)
perimeter = 2 * 14sqrt(2) + 28
perimeter = 28 + 28sqrt(2)
perimeter = 67.598 to 3 places, 67.6 to one place, 68 to the nearest whole number