Answer:
21.4
Step-by-step explanation:
We can solve for x using trigonometry
Here are the Trigonometric Ratios
Remember SOH CAH TOA
Sine = Opposite over Hypotenuse (SOH)
Cosine = Adjacent over Hypotenuse
Tangent = Opposite over Adjacent
We are given the measure of ∠T ( 72° )
We are also given the adjacent side length (6.6) ( Adjacent = the side length that is not the hypotenuse nor the opposite side length )
And we need to find the hypotenuse ( longest side length )
We this information we can use the trigonometric ratio Cosine to solve for x
That being said we want to set up an equation
(remember cosine = adjacent over hypotenuse )
[tex]cos(72)=\frac{6.6}{x}[/tex]
Now we solve for x
We can't get rid of the 6.6 itself so we want to multiply each side by x
now we have [tex]xcos(72)=6.6[/tex]
Step 2 divide each side by cos(72)
[tex]\frac{xcos(72)}{cos(72)} =x\\\frac{6.6}{cos(72)} \\x=\frac{6.6}{cos(72)}\\cos(72)=0.3090169944\\\frac{6.6}{0.3090169944} =21.35804865\\[/tex]
We're left with x = 21.35804865
Finally we want to round to the nearest tenth of a foot and we get that x = 21.4
