Question

Can somebody plz help?e

Answer 1

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 )

$cos(72)=\frac{6.6}{x}$

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)

$\frac{xcos(72)}{cos(72)} =x\\\frac{6.6}{cos(72)} \\x=\frac{6.6}{cos(72)}\\cos(72)=0.3090169944\\\frac{6.6}{0.3090169944} =21.35804865$

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