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Find the value of angle B, rounding to the nearest tenth of a degree.

Find the value of angle B, rounding to the nearest tenth of a degree.-example-1

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Law of Cosines.

- For a triangle ABC with sides labeled a,b, and c:


a^2=b^2+c^2-2bc\cos A
b^2=a^2+c^2-2ac\cos B
c^2=a^2+b^2-2ab\cos C

Since we are asked to look for angle B, we will use


b^2=a^2+c^2-2ac\cos B

Given:

a = 12 cm

b = 8 cm

c = 15 cm

Substituting the given values to our equation:


b^2=a^2+c^2-2ac\cos B
(8)^2=(12)^2+(15)^2-2(12)(15)\cos B
64=144+225-(360)\cos B
360\cos B=369-64
360\cos B=305
(360\cos B)/(360)=(305)/(360)
B=\cos ^(-1)(305)/(360)
B=32.089

Since we are asked to round the answer to its nearest tenth, the final answer would be 32.1 degrees.

User Tim Wayne
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