The angle the right side of the roof makes with the base is 34.67 degrees
How to determine the angle the right side of the roof makes with the base?
The given parameters are:
Base = 13.6
Left = 8.0
Angle between base and the left = 70 degrees
The sketch is added as an attachment
Start by calculating the length AC using:
AC^2 = AB^2 + BC^2 - 2 * AB * BC * cos(B)
This gives
AC^2 = 8^2 + 13.6^2 - 2 * 8* 13.6* cos(70)
Evaluate
AC^2 = 174.54
Take the square roots
AC = 13.21
The angle the right side of the roof makes with the base is then calculated as using the following laws of sines
AB/sin(C) = AC/sin(B)
This gives
8/sin(C) = 13.21/sin(70)
Evaluate
8/sin(C) = 14.06
This gives
sin(C) = 8/14.06
Evaluate
sin(C) = 0.5689
Take the arc sin of both sides
C = 34.67
Hence, the angle the right side of the roof makes with the base is 34.67 degrees
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