Question

Suppose that a roof is built so that the angle at the peak and the lengths of the sides, which differ, are known. How would the width of the house be determined?

Answer 1

Using the Law of Cosines.

As with many math problems, there are a number of ways this problem can be worked. Perhaps the most straightforward is to use the Law of Cosines to compute the side (c) opposite the given angle (C), given the sides (a, b) adjacent to that angle.

c² = a² + b² -2ab·cos(C)

Then the desired width of the house is ...

c = √(c²)

Answer 2

using the Law of Cosines

Explanation:

As with many math problems, there are a number of ways this problem can be worked. Perhaps the most straightforward is to use the Law of Cosines to compute the side (c) opposite the given angle (C), given the sides (a, b) adjacent to that angle.

c² = a² + b² -2ab·cos(C)

Then the desired width of the house is ...

c = √(c²)