Question

The roof of a house is being reconstructed to accommodate heavy snows. the current 32 foot roofline makes an 18.2° angle with the horizontal. the owner has decided to construct the new roof so that it makes a 50° with the horizontal as shown below. what will be the length of the new roofline?

Answer 1

To find the length of the new roofline, we can use the tangent function. The length is approximately 26.9 feet.

Step-by-step explanation:

To find the length of the new roofline, we can use the trigonometric function tangent. Let's call the length of the new roofline 'x'. The tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is the height of the roofline, which is 32 feet, and the adjacent side is the horizontal distance, which is 'x' feet. So, we can set up the equation:

tan(50°) = 32/x

To solve for 'x', we can multiply both sides of the equation by 'x' and then divide both sides by tan(50°). This gives us:

x = 32/tan(50°)

Using a calculator, we can find that tan(50°) ≈ 1.1917. So, substituting this value into the equation, we get:

x ≈ 32/1.1917

By calculating this, we find that the length of the new roofline is approximately 26.9 feet.

Answer 2

This is the concept of trigonometry, given that the current length of the roof is 32 ft, for use to get the adjusted length we need to get the adjacent distance;
cos theta=[adjacent]/[hypotenuse]
theta=18.2°
adjacent=a
hypotenuse=32
hence;
cos 18.2=a/32
a=32cos 18.2
a=30.4
When the angle was re-adjusted to 50 ° the new length will be given by:
cos 50=30.4/h
h=30.4/cos 50
h=47.29 ft
therefore the new roofline will be 47.29 ft