Question

What is the approximate value of x in the diagram below? (Hint: You will need

to use one of the trigonometric ratios given in the table.)

Answer 1

B. 39.59

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
`(opposite)/(hypotenuse)`. So let's plug in known values:

`sin(43) = (27)/(x)`

Multiply both sides by x

`sin(43) * x = 27`

divide both sides by sin(43)

`x=(27)/(sin(43))`

Normally I would use a calculator, but in this case I'll use the approximation given in the problem of 0.682

`x=(27)/(0.682)`

simplify the fraction

`x\approx39.59`