Te slope of the roof is 2/3. If the width of the house is 78 feet,what is the height of the roof, in feet? Assume the roof creates an isósceles triangle
half width is 39 feet
up 2/3 of 39
2 * 13 = 26 feet <----- answer
by the way, roofers go by pitch = height / full width so they would call this a pitch of 26/78 = 1/3
In an isosceles triangle, the two equal sides represent the height of the roof. The slope of the roof, which is the ratio of the vertical change to the horizontal change, is given as 2/3.
Let's represent the height of the roof as h feet. The width of the house is 78 feet.
Thus, we can set up the following equation:
h/78 = 2/3
To find h, we can cross-multiply:
3h = 2 * 78
3h = 156
Dividing both sides by 3:
h = 156/3
h = 52
Therefore, the height of the roof is 52 feet.
To find the height of the roof, we can use the formula for the slope of a line in mathematics, which is represented by the ratio of the vertical change (rise) to the horizontal change (run). In this case, the slope of the roof is given as 2/3.
The slope of a line is also equal to the tangent of the angle of inclination of the line. Since the roof creates an isosceles triangle, we know that the angle of inclination on either side of the roof is the same.
To find the height of the roof, we need to determine the length of the horizontal change (run). In this case, the width of the house is given as 78 feet, which represents the horizontal distance covered by the roof.
We will use the tangent function to find the height of the roof. The tangent of the angle of inclination (θ) is given by the formula:
tan(θ) = height of the roof / run = 2/3
Now, let's solve for the height of the roof:
Using the given information, the width of the house (run) is 78 feet.
tan(θ) = 2/3
By taking the inverse tangent (arctan) of both sides, we can find the angle of inclination (θ):
θ = arctan(2/3) ≈ 33.69 degrees
Now, we can use trigonometry to find the height of the roof. We know the angle of inclination (θ) is 33.69 degrees, and the width of the house (run) is 78 feet.
To find the height of the roof, we can use the following formula:
height of the roof = run * tan(θ)
height of the roof = 78 * tan(33.69)
height of the roof ≈ 78 * 0.6720
height of the roof ≈ 52.42 feet
Therefore, the height of the roof is approximately 52.42 feet.