Math / Geometry

QuestionFind $w x$ .
Write your answer as an integer or as a decimal rounded to the nearest tenth. $w x=$ $\square$ Submit

Studdy Solution

STEP 1

What is this asking? We need to find the length of one side of a right triangle, knowing an angle and another side. Watch out! Make sure your calculator is in degree mode, not radians!

STEP 2

1. Set up the trigonometric ratio
2. Calculate the length

STEP 3

Alright, let's dive into this triangle problem!
We're given a right triangle, so we can use our trigonometric friends – sine, cosine, and tangent!
We know the angle $\angle XWY$ is 21 degrees, and the side opposite to this angle is $WX$ , which we'll call $x$ for now.
We also know the side adjacent to the angle is $WY = \textbf{3.1}$ .
Which trigonometric friend uses the opposite and adjacent sides?
It's tangent, of course!

STEP 4

So, we can set up the equation: $\tan(21^\circ) = \frac{\text{opposite}}{\text{adjacent}} = \frac{x}{3.1}$ Remember, $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$ , where $\theta$ is the angle.

STEP 5

Now, we want to solve for $x$ , the length of side $WX$ .
To do that, we'll multiply both sides of our equation by 3.1: $3.1 \cdot \tan(21^\circ) = 3.1 \cdot \frac{x}{3.1}$ On the right side, the 3.1's divide to one, leaving us with: $x = 3.1 \cdot \tan(21^\circ)$

STEP 6

Now, grab your calculator, make sure it's in degree mode, and calculate the value: $x = 3.1 \cdot \tan(21^\circ) \approx 3.1 \cdot \textbf{0.38386} \approx \textbf{1.18997}$ Rounding to the nearest tenth gives us $x \approx \textbf{1.2}$ .
Boom!

STEP 7

The length of $WX$ is approximately 1.2.

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