Question

About how wide is this house?

Answer 1

Answer:

The house is 37.37 feet wide.

Step-by-step explanation:

See the diagram attached to this question.

We know, the formula from properties of triangle that

$\cos A = \frac{b^{2} + c^{2} - a^{2}}{2bc}$

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

$\cos 65 = \frac{26^{2} + 40^{2} - x^{2}}{2\times 26 \times 40}$

⇒$26^{2} + 40^{2} - x^{2} = 2 \times 26 \times 40 \cos 65 = 879$

⇒ $x^{2} = 26^{2} + 40^{2} - 879 = 1396.95$

⇒ x = 37.37 feet.

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