Question

About how wide is this house?

Answer 1

The house is 37.37 feet wide.

Explanation:

See the diagram attached to this question.

We know, the formula from properties of triangle that

`\cos A = (b^(2) + c^(2) - a^(2))/(2bc)`

Here we assume that A = 65°, b = 26 feet and c = 40 feet and we have to find a = x feet.

So, using this above formula, we can write

`\cos 65 = (26^(2) + 40^(2) - x^(2))/(2* 26 * 40)`

⇒
`26^(2) + 40^(2) - x^(2) = 2 * 26 * 40 \cos 65 = 879`

⇒
`x^(2) = 26^(2) + 40^(2) - 879 = 1396.95`

⇒ x = 37.37 feet.

Therefore, the house is 37.37 feet wide. (Answer)