Answer:
x = 36.27
Step-by-step explanation:
By using the steps to find sin θ backwards, we can find x, the hypotenuse.
sin θ = [tex]\frac{opposite}{hypotenuse}[/tex] or side [tex]\frac{a}{c}[/tex] (as seen in my example picture).
We already know the value for sin (α), which is 32° because its given. The opposite side (a) is 20 and the hypotenuse side (c) is x which are both also given.
So the equation now looks like:
sin 32° = [tex]\frac{20}{x}[/tex]
Don't solve for the sin 32 yet! First, we have to isolate the variable.
To get rid of the x in the denominator you have to multiply both sides by x:
( sin 32 ) · x = ( [tex]\frac{20}{x}[/tex] ) · x
( sin 32 ) x = 20
Then, you have to divide both sides by sin 32 to get x by itself:
(( sin 32 ) x ) ÷ ( sin 32 ) = 20 ÷ ( sin 32 )
x = 20 ÷ ( sin 32 )
Lastly, you have to use a calculator to find 20 ÷ ( sin 32 ), and it should give you 36.2695543766.
The question asks you to round to 2 decimal places so:
x = 36.27
