A triangle has sides of length 7 cm, 12 cm, and 15 cm. What is the measure of the angle opposite the side that is 7 cm long? Round to the nearest degree. 27° 42° 63° 77°

Answer:Given : A triangle has sides of length 7 cm, 12 cm, and 15 cm.

To find : Angle opposite the side that is 7 cm long? Round to the nearest degree.

Solution : We have a triangle of sides a=7 cm, b = 12 cm, c=15 cm.

By using cosine rule : a² = b²+c² - 2 bc cos (A).

Where angle A is opposite to side a=7 cm.

Plugging the values in formula,

(7) ² = (12) ² + (15) ² - 2 (12) (15) cos (A).

49 = 144 + 225 - 360 cos (A).

49 = 369 - 360 cos (A).

-320 = - 360 cos (A).

On dividing by - 360 and switching side

A = cos^{-1} (0.89) = 27 / degrees.

Therefore, angle opposite the side that is 7 cm is 27 degrees.