Question

A roofer sketches a diagram of a house on which he is working.

Based on the diagram, about how wide is the house?
28.5 ft.
37.4 ft.
42.9 ft.
56.2 ft.

Answer 1

(B)37.4 feet

Explanation:

From he given diagram, let width of the house be x, then using the cosine formula, we get

`x^2=(40)^2+(26)^2-2(40)(26)cos65^(\circ)`

=
`1600+676-2080(0.422)`

=
`2276-877.76`

=
`1398.24`

Thus,
`x^2=1398.24`

⇒
`x=√(1398.24)`

⇒
`x=37.4 ft`

Therefore, the width of the house is 37.4 feet.

Answer 2

Using the SSA formula:

X = SQRT ( 40^2 + 26^2 - 2*40*26*cos(65))

X = SQRT(2276 - 2080*cos(65))

X = SQRT(1396.954)

X = 37.37 = 37.4 ft.