A cottage under construction is to be 15.6m wide. The two sides of the roof are to be supported by equal rafters that meet at a 52 degree angle. Determine the length of the rafters to the nearest cm using a) the cosine law b) the sine law
I am not understanding this question at all. please help. thanks.
Sure, I can help you understand the question!
The given problem is about determining the length of the rafters for a cottage under construction. The cottage is 15.6 meters wide, and the two sides of the roof are supported by equal rafters that meet at a 52-degree angle. The goal is to find the length of the rafters using both the cosine law and the sine law.
Let's begin by understanding the cosine law:
a) The Cosine Law:
The cosine law states that the square of one side of a triangle is equal to the sum of the squares of the other two sides, minus twice the product of those sides and the cosine of the included angle.
In our case, we have a triangle formed by the two rafters and the width of the cottage. Let's label the width of the cottage as "c" and the length of the rafters as "a."
Using the cosine law, we can write the equation as follows:
a^2 = c^2 + c^2 - 2c * c * cos(52°)
Now, we can solve for "a" by substituting the given values into the equation and calculating the result.
b) The Sine Law:
The sine law relates the ratios of the lengths of the sides of a triangle to the sines of their opposite angles. It states that the ratio of the length of a side of a triangle to the sine of its opposite angle is equal for all sides and angles of the triangle.
In our case, we can use the sine law to find the length of the rafters:
sin(52°) / c = sin(90°) / a
Here, we can substitute the given values and solve for "a" as well.
By using both the cosine law and the sine law, we can compare the results and verify the accuracy of our calculations. Also, remember to round your final answer to the nearest cm, as mentioned in the question.
I hope that helps! If you have any more questions or if anything is unclear, please feel free to ask.