Question

Solve a triangle with a =5, b =6, and c = 7. Round to the nearest tenth.

Answer 1

<A ≈ 45 degrees

<B ≈ 57 degrees

<C ≈ 78 degrees

Explanation:

Hi there!

1) Find <C with the law of cosines

Typically, we want to solve for the angle opposite the largest side first.

Law of cosines:
`cosC=(a^2+b^2-c^2)/(2(a)(b))`

Plug in given values

`cosC=(5^2+6^2-7^2)/(2(5)(6))\\cosC=(1)/(5)\\C=cos^-^1((1)/(5) )\\C=78`

Therefore, <C is approximately 78 degrees.

2) Find <B with the law of cosines

`cosB=(a^2+c^2-b^2)/(2(a)(c))`

Plug in given values

`cosB=(5^2+7^2-6^2)/(2(5)(7))\\cosB=(19)/(35)\\B=cos^-^1((19)/(35))\\B=57`

Therefore, <B is approximately 57 degrees.

3) Find <A

The sum of the interior angles of a triangle is 180 degrees. To solve for <A, subtract <B and <C from 180:

180-57-78

= 45

Therefore, <A is 45 degrees.

I hope this helps!