A cottage under construction is to be 12.6m wide. The two sides of the roof are to be supported by rafters that meet at an angle of 50°. How long should the rafters be if they are the same length?
If you really mean meet at 50 degrees at peak (like very steep)
rafter 25 degrees from vertical, horizontal length = 6.3
so
sin 25 = 6.3/h
To find the length of the rafters, we can use trigonometry. Let's consider one side of the roof.
We have a right triangle, where the width of the cottage is the base, the length of the rafter is the hypotenuse, and the angle between the base and hypotenuse is given as 50°.
Using the sine function, we can write:
sin(50°) = Opposite / Hypotenuse
The opposite side is half the width of the cottage since both sides of the roof are supported by rafters of the same length. Therefore, the opposite side is (12.6m / 2) = 6.3m.
Substituting these values into the equation:
sin(50°) = 6.3m / Hypotenuse
To find the length of the rafters, we rearrange the equation and solve for the hypotenuse:
Hypotenuse = 6.3m / sin(50°)
Now, let's calculate the length of the rafters:
Hypotenuse = 6.3m / sin(50°)
Hypotenuse ≈ 8.02m (rounded to two decimal places)
Therefore, the length of each rafter should be approximately 8.02 meters.
To find the length of the rafters, we can use trigonometry, specifically the sine function.
First, we need to identify the triangle formed by the rafter and the walls of the cottage. Let's call the length of the rafters "x". The 50° angle is opposite to the side we want to find.
Since we have the opposite side length and the angle, we would use the sine function, which is defined as the ratio of the length of the opposite side to the length of the hypotenuse:
sin(angle) = opposite / hypotenuse
Applying this to our triangle:
sin(50°) = 12.6 / x
Next, we can rearrange the equation to solve for x:
x = 12.6 / sin(50°)
Now we can calculate the length of the rafters by substituting the value of the angle into the equation:
x ≈ 12.6 / sin(50°) ≈ 16.04 meters (rounded to two decimal places)
Therefore, if the rafters are the same length, they should be approximately 16.04 meters long.