Question

Help please! Find the difference between the measure of the largest angle and the measure of the smallest angle in the triangle above.

A.14° B.45° C.88..9° D.99.8°

Answer 1

We will use the Cosine law:
c² = a² + b² - 2 a b cos C
In this case:
15² = 10² + 7² - 2 · 10 · 7 cos K
225 = 100 + 49 - 140 cos K
76 = - 140 cos K
cos K = - 76 / 140
cos K = - 0.5428
∠ K= cos ^(-1) ( -0.5428 ) = 122.88° ( the largest angle )
49 = 100 + 225 - 2 · 10 · 15 cos J
- 276 = -300 cos J
cos J = 0.92
∠J = cos ^(-1) 0.92 = 23.08° ( the smallest angle )
122.8° - 23.08° = 99.8°
Answer: D )