Answer:
B. 39.59
Step-by-step explanation:
So 43 degrees, you know the length of the opposite side (27) and the angle (43 degrees), the only unknown is the hypotenuse. So you're looking for a trigonometric ratio that uses the angle (all of them do, except technically the inverse don't), the opposite side, and the hypotenuse. Sine is defined as [tex]\frac{opposite}{hypotenuse}[/tex]. So let's plug in known values:
[tex]sin(43) = \frac{27}{x}[/tex]
Multiply both sides by x
[tex]sin(43) * x = 27[/tex]
divide both sides by sin(43)
[tex]x=\frac{27}{sin(43)}[/tex]
Normally I would use a calculator, but in this case I'll use the approximation given in the problem of 0.682
[tex]x=\frac{27}{0.682}[/tex]
simplify the fraction
[tex]x\approx39.59[/tex]
