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# law of cosines math help word problem!?

building inspector julie wang checks a building in the shape of a regular octagon each side is 20 ft long. she checks that the owner has located the corners of the foundation correctly calculate what the lengths of the diagonals hb, hc, and hd shouldbe. link to drawing:

### 2 Answers

- tcLv 77 years agoFavorite Answer
<HAB = 180(8-2) / 8 = 135

<HBC = 135 - 22.5 = 112.5

<HCB = 180 - 135 = 45 => <HBC and <HCB are supplementary

<HCD = 135 - 45 = 90

HB^2 = 20^2 +20^2 - 2*20*20 cos135

HB = 36.96

HC^2 = 20^2 + 36.96^2 - 2*20*36.96cos112.5

HC = 48.29

HD^2 = 20^2 + 48.29^2

HD = 52.27

- moatzLv 44 years ago
a/sinA = b/sinB = c/sinC you comprehend A = 15.7, B = ninety so C = a hundred and eighty-ninety-15.7 = seventy 4.3 1450/sin15.7 = c/sin74.3 remedy for c c=(1450/sin15.7)*sin74.3 c=5358.40 5*0.ninety six c=(aprox) 5158.fifty 3 around as much as 5159 it is mockingly answer c.