Question

71) How long is the wire to the nearest foot?A. 40 ftB. 50 ftC. 64 ftD. 78 ft

Answer 1

B

71) As we have a right triangle, one leg and another missing then we can use a trigonometric ratio to find that out.

Note that the missing leg is the hypotenuse (opposite to the right angle):

`\begin{gathered} \sin (64^(\circ))=\frac{\text{opposite side}}{hypotenuse} \\ \sin (64^(\circ))=(45)/(x) \\ \sin (64^(\circ))x\text{ =45} \\ (\sin (64^(\circ))x)/(\sin (64^(\circ)))=(45)/(\sin (64^(\circ))) \\ x\approx50 \end{gathered}`

2) Note that we've crossed multiplied and then divided both sides by the same quantity sin(64)

3) Hence, the missing side (hypotenuse) is approximately 50 ft