Question

It’s not 50.5 which is what I keep getting.

Answer 1

Explanation:

`cos C=(20^2+18^2-22^2)/(2 * 20 * 18) =(20^2+(18+22)(18-22))/(2 * 20 * 18) \\=(20^2+40(-4))/(2 * 20 * 18) \\=(400-160)/(720) \\=(240)/(720) \\=(1)/(3) \\C=cos^(-1)((1)/(3) )\\\approx 70.5^\circ`

Answer 2

∠ C ≈ 70.5°

Explanation:

using the Law of Cosines

c² = a² + b² - 2ab cosC

where c is the side opposite ∠ C and a, b the sides adjacent to ∠ C

here a = 20, b = 18 , c = 22 , then substituting into the formula

22² = 20² + 18² - ( 2 × 20 × 18 × cosC )

484 = 400 + 324 - 720cosC

484 = 724 - 720cosC ( subtract 724 from both sides )

- 240 = - 720 cosC ( divide both sides by - 720 )

`(-240)/(-720)` = cosC , that is

cosC = 0.3333 , then

∠ C =
`cos^(-1)` (0.3333) ≈ 70.5° ( to the nearest tenth )