Math  /  Trigonometry

QuestionSolve for xx in the triangle. Round your answer to the nearest tenth. 5555^{\circ} 1212 xx

Studdy Solution

STEP 1

What is this asking? We need to find the length of the side xx in a right triangle, knowing one angle is 5555^\circ and the adjacent side is 1212. Watch out! Make sure your calculator is in degree mode, not radians!
Also, remember SOH CAH TOA.

STEP 2

1. Set up the tangent equation.
2. Solve for xx.
3. Round to the nearest tenth.

STEP 3

Remember **SOH CAH TOA**.
Since we know the **adjacent** side to the 5555^\circ angle and we want to find the **opposite** side, we'll use the **tangent** function.
Tangent is defined as tan(θ)=oppositeadjacent\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}.

STEP 4

In our triangle, the **angle** θ\theta is 5555^\circ, the **opposite** side is xx, and the **adjacent** side is 1212.
Let's plug these values into the **tangent formula**: tan(55)=x12 \tan(55^\circ) = \frac{x}{12}

STEP 5

To **isolate** xx, we need to multiply both sides of the equation by 1212: 12tan(55)=12x12 12 \cdot \tan(55^\circ) = 12 \cdot \frac{x}{12}

STEP 6

On the right side, the 1212 in the numerator and the 1212 in the denominator divide to one, leaving us with: 12tan(55)=x 12 \cdot \tan(55^\circ) = x

STEP 7

Now, grab your calculator and make sure it's in **degree mode**!
Calculate 12tan(55)12 \cdot \tan(55^\circ): x121.428=17.136 x \approx 12 \cdot 1.428 = 17.136

STEP 8

The problem asks us to round to the nearest tenth.
Looking at our result 17.13617.136, the digit in the **tenths place** is 11, and the digit to the right of it is 33.
Since 33 is less than 55, we round **down**, keeping the 11 as is.

STEP 9

So, our **final rounded answer** is approximately 17.117.1.

STEP 10

The length of side xx is approximately 17.117.1.

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