Studdy AI Logo
Math  /  Geometry

QuestionFind vXv X.
Write your answer as an integer or as a decimal rounded to the nearest tenth. vx=v x= □\square Suhmit

Studdy Solution

STEP 1

What is this asking? We need to find the length of the hypotenuse of a right triangle, given one side length and an angle. Watch out! Don't mix up sine and cosine!
Remember SOH CAH TOA!

STEP 2

1. Set up the trigonometric ratio.
2. Solve for the unknown side.

STEP 3

Alright, let's dive in!
We've got a right triangle, a known angle, and a known side.
This screams trigonometry!
We're trying to find the hypotenuse, VX‾\overline{VX}, and we know the side adjacent to our angle, WX‾\overline{WX}.
Which trig function relates the adjacent side and the hypotenuse?
It's the **cosine**!

STEP 4

Remember SOH CAH TOA!
Cosine is **Adjacent** over **Hypotenuse**.
So, we can set up our equation like this: cos⁡(27∘)=WX‾VX‾\cos(27^\circ) = \frac{\overline{WX}}{\overline{VX}} We know WX‾=2\overline{WX} = 2, so let's plug that in: cos⁡(27∘)=2VX‾\cos(27^\circ) = \frac{2}{\overline{VX}}

STEP 5

Now, we want to get VX‾\overline{VX} all by itself.
To do this, we can multiply both sides of the equation by VX‾\overline{VX}: VX‾⋅cos⁡(27∘)=VX‾⋅2VX‾\overline{VX} \cdot \cos(27^\circ) = \overline{VX} \cdot \frac{2}{\overline{VX}} On the right side, the VX‾\overline{VX} terms divide to one, leaving us with: VX‾⋅cos⁡(27∘)=2\overline{VX} \cdot \cos(27^\circ) = 2

STEP 6

Next, we'll divide both sides by cos⁡(27∘)\cos(27^\circ) to isolate VX‾\overline{VX}: VX‾⋅cos⁡(27∘)cos⁡(27∘)=2cos⁡(27∘)\frac{\overline{VX} \cdot \cos(27^\circ)}{\cos(27^\circ)} = \frac{2}{\cos(27^\circ)} Again, we can divide to one: VX‾=2cos⁡(27∘)\overline{VX} = \frac{2}{\cos(27^\circ)}

STEP 7

Now, grab your calculator and find the value of cos⁡(27∘)\cos(27^\circ), which is approximately **0.891**.
Let's plug that in: VX‾=20.891\overline{VX} = \frac{2}{\textbf{0.891}}

STEP 8

Finally, perform the division: VX‾≈2.244668911\overline{VX} \approx 2.244668911 Rounding to the nearest tenth gives us our **final result**: VX‾≈2.2\overline{VX} \approx \textbf{2.2}

STEP 9

The length of VXVX is approximately **2.2**.

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord