Question

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

Answer 1

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.

Answer 2

Answer:

(B)37.4 feet

Step-by-step 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, $x^2=1398.24$

⇒$x=\sqrt{1398.24}$

⇒$x=37.4 ft$

Therefore, the width of the house is 37.4 feet.