Question

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

Answer 1

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 $\frac{opposite}{hypotenuse}$. So let's plug in known values:

$sin(43) = \frac{27}{x}$

Multiply both sides by x

$sin(43) * x = 27$

divide both sides by sin(43)

$x=\frac{27}{sin(43)}$

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

$x=\frac{27}{0.682}$

simplify the fraction

$x\approx39.59$