To find the length of one side of the A-frame cabin's roof, use the cosine of the 60° angle and half the width of the cabin (17.5 feet) as input in the trigonometric ratio.
The resulting length of the roof side, or the hypotenuse of the triangle, is 35 feet.
To find the length of one side of the roof from the ground level to the peak in an A-frame cabin, we can use trigonometric ratios.
Given that the roof makes a 60° angle with the base and that the cabin is 35 feet wide, we can consider one half of the width (35 feet / 2 = 17.5 feet) as the base of a right triangle, where the roof side is the hypotenuse.
Using the cosine function which is defined as adjacent over hypotenuse (cos(θ) = adjacent/hypotenuse), we can write:
cos(60°) = (17.5 feet) / hypotenuse
Since cos(60°) = 0.5, the equation becomes:
0.5 = (17.5 feet) / hypotenuse
By solving for hypotenuse, we get:
hypotenuse = (17.5 feet) / 0.5
hypotenuse = 35 feet
Thus, the length of one side of the roof from its ground level to the peak is 35 feet, which is the length of the hypotenuse in the right triangle.