A cottage under construction is to be 12.6 meters wide. The two sides of the roof are to be supported by rafters that meet at a 50 degree angle.How long should the rafters be?

sin 25 = 6.3/L

solve for L

However, being mathematicians and not carpenters, we left no overhang beyond the walls and the water will run down the walls and peel the paint and flood the basement :)

To find the length of the rafters, we can use trigonometry. The given angle is 50 degrees and the width of the cottage is 12.6 meters.

1. We can start by visualizing the situation. Imagine a right triangle, with the width of the cottage as the base, and the length of the rafters as the hypotenuse. The angle between the base and the hypotenuse is 50 degrees.

2. The trigonometric function that relates the length of the adjacent side (the base) to the hypotenuse and the angle is cosine (cos). Since we want to find the length of the hypotenuse (the rafters), we can use the formula:

cos(angle) = adjacent / hypotenuse

3. Rearranging the formula to solve for the hypotenuse, we have:

hypotenuse = adjacent / cos(angle)

4. Plugging in the values we know, the adjacent side (width of the cottage) is 12.6 meters, and the angle is 50 degrees. So, we get:

hypotenuse = 12.6 meters / cos(50)

Now, we need to calculate the value of cos(50). This can be done using a scientific calculator or a trigonometric table.

5. Evaluating cos(50), we find that it is approximately 0.6428.

6. Substituting this value back into the formula, we can calculate the length of the rafters:

hypotenuse = 12.6 meters / 0.6428

7. Solving the equation, we get:

hypotenuse ≈ 19.58 meters

Therefore, the rafters should be approximately 19.58 meters long.