Math / Trigonometry

QuestionSolve for $x$ . Round to the nearest tenth, if necessary.
Answer Attempt 2 out of 2 $x=$ $\square$

Studdy Solution

STEP 1

What is this asking? We need to find the length of the side $x$ in a right triangle, knowing one angle and the length of the side adjacent to it. Watch out! Make sure your calculator is in degree mode, not radians!
Also, remember SOH CAH TOA.

STEP 2

1. Set up the trigonometric ratio
2. Solve for $x$

STEP 3

Alright, let's dive in!
We've got a right triangle, a known angle, and we're looking for a side length.
That screams trigonometry!
We know the angle $72^\circ$ and the side adjacent to it, which is $3.9$ .
We're looking for the hypotenuse, $x$ .
Which trig function relates the adjacent side and the hypotenuse?
It's cosine!

STEP 4

So, we can set up the equation: $\cos(72^\circ) = \frac{\text{adjacent}}{\text{hypotenuse}}$ $\cos(72^\circ) = \frac{3.9}{x}$

STEP 5

Now, let's isolate $x$ .
We can multiply both sides of the equation by $x$ , which gives us: $x \cdot \cos(72^\circ) = 3.9$

STEP 6

To get $x$ by itself, we'll divide both sides by $\cos(72^\circ)$ : $x = \frac{3.9}{\cos(72^\circ)}$

STEP 7

Time to crunch the numbers!
Using a calculator (make sure it's in degree mode!), we find that $\cos(72^\circ) \approx 0.309$ .
So, $x \approx \frac{3.9}{0.309}$ $x \approx 12.6213592233$

STEP 8

The problem asks us to round to the nearest tenth, so our final answer is approximately $12.6$ .

STEP 9

$x \approx 12.6$

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