An A-frame house is 40 feet high and 30 feet wide. Find the angle that the roof makes with the floor. Round the angle nearest degree.
To find the angle that the roof makes with the floor in an A-frame house, we can use trigonometry. In this case, we are dealing with a right triangle, where the height of the house is the vertical side (opposite angle θ), the width of the house is the base (adjacent to angle θ), and the roof is the diagonal side (hypotenuse).
We can use the tangent function, which is the ratio of the opposite side to the adjacent side, to find the angle θ. The tangent function is defined as:
tan(θ) = opposite / adjacent
In this case, the opposite side is the height of the house (40 ft) and the adjacent side is half of the width of the house (30 ft / 2 = 15 ft). Plugging in these values, we have:
tan(θ) = 40 ft / 15 ft
Using a calculator or trigonometry table, we can find the value of θ by taking the inverse tangent (arctan) of both sides:
θ = arctan(40 ft / 15 ft)
Calculating this using a calculator, we get:
θ ≈ 67.38 degrees
Therefore, the angle that the roof makes with the floor in the A-frame house is approximately 67 degrees when rounded to the nearest degree.
To find the angle that the roof makes with the floor, we can use the inverse tangent function. The height of the A-frame house forms one side of a right triangle, with the width of the house forming the base.
Using the equation:
angle = inverse tan(height / base)
Substituting the given values:
angle = inverse tan(40 / 30)
Calculating the tangent:
angle = inverse tan(1.333)
Using a scientific calculator or online tool to find the inverse tangent of 1.333:
angle ≈ 53.13 degrees
Rounding to the nearest degree:
angle ≈ 53 degrees
Therefore, the angle that the roof makes with the floor is approximately 53 degrees.