Answer :
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
[tex]\cos A = \frac{b^{2} + c^{2} - a^{2}}{2bc}[/tex]
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
[tex]\cos 65 = \frac{26^{2} + 40^{2} - x^{2}}{2\times 26 \times 40}[/tex]
⇒[tex]26^{2} + 40^{2} - x^{2} = 2 \times 26 \times 40 \cos 65 = 879[/tex]
⇒ [tex]x^{2} = 26^{2} + 40^{2} - 879 = 1396.95[/tex]
⇒ x = 37.37 feet.
Therefore, the house is 37.37 feet wide. (Answer)