Question

If AB = 13, BC = 9, and CA = 17, list the angles of
in order from smallest to largest.

Answer 1

Solving for the angles, we need to apply and use Law of Cosines:
Solving for ∠AB, we have
cos ∠AB = (BC² + CA² - AB²) / 2*BC*CA
cos∠AB = (9²+17² -13²) / 2*17*9
∠AB = 48.94°

Solving for ∠BC, we have
cos ∠BC = (AB² + CA² - BC²) / 2*AB*CA
cos∠AB = (13²+17² -9²) / 2*17*13
∠BC = 31.47°

Solving for angle CA, we have:
∠CA = 180° - 31.47° - 48.94°
∠CA = 99.49°

The smallest angle is 31.47°.

Answer 2

The angles are A = 31.47⁰, B = 99.59⁰ and C = 48.94⁰

Explanation:

We have cosine formula
`cosA=(AB^2+AC^2-BC^2)/(2* AB* AC)`

Using cosine formula,

`cosA=(13^2+17^2-9^2)/(2* 13* 17)=0.853\\\\A=31.47^0`

`cosB=(13^2+9^2-17^2)/(2* 9* 13)=-0.167\\\\B=99.59^0`

`cosC=(9^2+17^2-13^2)/(2* 9* 17)=0.657\\\\C=48.94^0`

So the angles are A = 31.47⁰, B = 99.59⁰ and C = 48.94⁰.