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.
