Question

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

Answer 1

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.