Math  /  Trigonometry

QuestionSolve for xx. Round to the nearest tenth, if necessary.
Answer Attemptiout of 2 x=x=

Studdy Solution

STEP 1

What is this asking? We need to find the length of the side xx in a right triangle, knowing an angle and another side. 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 xx.
3. Round to the nearest tenth.

STEP 3

Alright, let's **do this**!
We've got a right triangle, an angle, and we want to find a side.
That's trigonometry time!
We know the angle 2626^\circ at HH, and we know the side *adjacent* to it is HF=2HF = 2.
The side we *want* to find is GF=xGF = x, which is *opposite* the angle.
Adjacent and opposite?
That screams "**tangent**" to me!
Remember SOH CAH TOA?
Tangent is Opposite over Adjacent!

STEP 4

So, we can write: tan(26)=oppositeadjacent=x2 \tan(26^\circ) = \frac{\text{opposite}}{\text{adjacent}} = \frac{x}{2} Boom! We've got our equation set up!

STEP 5

Now, we want to get xx all by itself.
It's being divided by 22, so we need to **multiply both sides** of the equation by 22.
This gives us: 2tan(26)=2x2 2 \cdot \tan(26^\circ) = 2 \cdot \frac{x}{2}

STEP 6

On the right side, the 22 in the numerator and the 22 in the denominator divide to one, leaving us with just xx: 2tan(26)=x 2 \cdot \tan(26^\circ) = x

STEP 7

Now, grab your calculator and make sure it's in **degree mode**!
Calculate 2tan(26)2 \cdot \tan(26^\circ): x=2tan(26)20.48770.9754 x = 2 \cdot \tan(26^\circ) \approx 2 \cdot 0.4877 \approx 0.9754

STEP 8

The problem asks us to round to the nearest tenth.
Looking at our result 0.97540.9754, the digit in the tenths place is 99, and the digit to the right of it is 77.
Since 77 is greater than or equal to 55, we round up.
So, 0.97540.9754 rounded to the nearest tenth is approximately 1.01.0.

STEP 9

x1.0x \approx 1.0

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