Atriangle 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. 29 pts and brainliest if youre correct.

Angle opposite the side that is 7 cm is 27 degrees.

Step-by-step explanation:

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 sides

     .

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

a is the right answer