Question

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

Answer 1

Answer:

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

Step-by-step explanation:

We have cosine formula $cosA=\frac{AB^2+AC^2-BC^2}{2\times AB\times AC}$

Using cosine formula,

     $cosA=\frac{13^2+17^2-9^2}{2\times 13\times 17}=0.853\\\\A=31.47^0$

     $cosB=\frac{13^2+9^2-17^2}{2\times 9\times 13}=-0.167\\\\B=99.59^0$

     $cosC=\frac{9^2+17^2-13^2}{2\times 9\times 17}=0.657\\\\C=48.94^0$

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

Answer 2

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°.