A carpenter is building a house. He is constructing the roof. The roof has an angle of elevation of 40° from the horizontal. The height he wants to make the roof is 18 feet. How far is it from the bottom edge of the roof to the top of the roof? (Find the hypotenuse to the nearest hundredth)
draw a diagram. If the distance is x,
18/x = sin40°
plug and chug to solve for x
To find the distance from the bottom edge of the roof to the top of the roof, we need to use trigonometry. The angle of elevation and the height of the roof form a right triangle, where the height is the opposite side and the distance we're looking for is the hypotenuse.
We can use the trigonometric function tangent (tan) to determine the length of the top edge. The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side.
The formula for tangent is: tan(angle) = opposite/adjacent.
In this case, the angle of elevation is 40°, and the height of the roof is 18 feet. We want to find the length of the adjacent side, which is the distance from the bottom edge of the roof to the top of the roof.
Thus, we rearrange the formula to solve for the adjacent side:
adjacent = opposite / tan(angle).
Now we can plug in the values:
adjacent = 18 feet / tan(40°).
To find the value of tan(40°), you can use a scientific calculator or an online tool capable of calculating trigonometric functions.
After finding the tangent value, divide 18 feet by that value to get the length of the adjacent side (the distance from the bottom edge of the roof to the top).
Rounding the result to the nearest hundredth will give you the distance in feet from the bottom edge of the roof to the top of the roof.