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°

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.

Hello! The correct answer is 27 degrees.

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