Explanation:
Use distance formula to find the lengths of the sides.
a = √((8 − (-7))² + (-6 − (-4))²) = √229
b = √((8 − (-8))² + (-6 − (-5))²) = √257
c = √((-7 − (-8))² + (-4 − (-5))²) = √2
Use law of cosine to find one of the angles.
c² = a² + b² − 2ab cos C
(√2)² = (√229)² + (√257)² − 2(√229)(√257) cos C
2 = 229 + 257 − 2√58853 cos C
cos C = 242/√58853
C = 4.018°
To find the second angle, either use law of sines, or use law of cosine again. Using law of cosine:
b² = a² + c² − 2ac cos B
(√257)² = (√229)² + (√2)² − 2(√229)(√2) cos B
257 = 229 + 2 − 2√458 cos B
cos B = -13/√458
B = 127.405°
Finally, find the third angle using sum of angles of a triangle, or law of sines, or law of cosine. Using law of cosine:
a² = b² + c² − 2bc cos A
(√229)² = (√257)² + (√2)² − 2(√257)(√2) cos A
229 = 257 + 2 − 2√514 cos A
cos A = 15/√514
A = 48.576°