An a-frame cabin is 38 feet across at the base and the roof males an angle of 52 degrees with the ground how tall is the cabin?
To find the height of the A-frame cabin, we can use basic trigonometry. The given information is that the cabin is 38 feet across at the base, and the roof makes an angle of 52 degrees with the ground.
We can visualize the situation by drawing a right triangle, where the base of the cabin forms one side, the height of the cabin forms another side, and the roof of the cabin forms the hypotenuse.
Using the trigonometric function tangent (tan), we can write the equation:
tan(52 degrees) = height of the cabin / 38 feet
To find the height of the cabin, we need to isolate it. We can rearrange the equation by multiplying both sides by 38 feet:
height of the cabin = 38 feet * tan(52 degrees)
Now, we can calculate the height by plugging the values into a calculator:
height of the cabin ≈ 38 feet * tan(52 degrees)
height of the cabin ≈ 38 feet * 1.2799
height of the cabin ≈ 48.761 feet
Therefore, the height of the A-frame cabin is approximately 48.761 feet.