The angle that the right side of the roof makes with the base of the roof to the nearest degree is 32 degrees.
We know that a triangle is a three sided figure. The question shows us that the left side of the triangular roof is 8.0 m long and makes an angle of 70 degrees with the base of the roof. This base has a length of 13.6 m.
We can now make use of the cosine rule;
b^2 = a^2 + c^2 - 2ac cos B
a = 13.6
b = ?
c = 8
B = 70 degrees
Now;
b = √(13.6)^2 + (8)^2 - 2(13.6 * 8) cos 70
b = √184.96 + 64 - 2(108.8) * 0.3420
b = √184.96 + 64 - 44.42
b = 14.3
By the use of the sine rule;
b/sinB = c/sinC
14.3/sin70 = 8/sinC
14.3 * sinC = 8 * sin70
sinC = 8 * sin70/14.3
C = 32 degrees
The angle that the right side of the roof makes with the base of the roof to the nearest degree is 32 degrees.
Learn more about cosine rule:https://brainly.com/question/20839703
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