Question

A common design for a mountain cabin is an A-frame

Answer 1

Answer:

54.98 degrees.

Step-by-step explanation:

In the diagram, the sides of the A-Frame are lengths AB and BC. The width of the cabin is length BC. We are to determine the measure of the angle at B, i.e. the angle between the two sides of the roof.

Using Cosine Rule:

$b^2=a^2+c^2-2acCos B\\Cos B=\dfrac{b^2-a^2-c^2}{-2ac} \\B=arcCos(\dfrac{b^2-a^2-c^2}{-2ac} )\\a=26, b=24, c=26\\B=arcCos(\dfrac{24^2-26^2-26^2}{-2*26*26} )\\=arcCos 0.5739\\B=54.98^0$

The angle in between the two sides of the roof is 54.98 degrees.