Question

Can somebody plz help?e

Answer 1

21.4

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 )

`cos(72)=(6.6)/(x)`

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
`xcos(72)=6.6`

Step 2 divide each side by cos(72)

`(xcos(72))/(cos(72)) =x\\(6.6)/(cos(72)) \\x=(6.6)/(cos(72))\\cos(72)=0.3090169944\\(6.6)/(0.3090169944) =21.35804865\\`

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