An A-frame house is 45 feet high and 32 feet wide. Find the measure of the angle that the roof makes with the floor. Round to the nearest degree.
let the angle be Ø
tanØ = 45/32
Ø = arctan(45/32) = 54.58 or 55°
To find the measure of the angle that the roof makes with the floor in an A-frame house, we can make use of trigonometry. The roof and the floor form a right triangle, where the height of the A-frame house is the vertical side (opposite side) and the width is the base (adjacent side).
We can use the tangent function to find the angle, as tangent is defined as the ratio of the opposite side to the adjacent side in a right triangle.
In this case, the opposite side is the height of the A-frame house, which is 45 feet, and the adjacent side is the width, which is 32 feet.
Therefore, the tangent of the angle θ is given by:
tan(θ) = opposite/adjacent
tan(θ) = 45/32
To find the measure of the angle, we need to take the inverse tangent (or arctan) of both sides:
θ = arctan(45/32)
Using a scientific calculator or online calculator with the arctan function, we can determine that the angle is approximately 55.5 degrees.
Therefore, the measure of the angle that the roof makes with the floor is approximately 55.5 degrees (rounded to the nearest degree).