Math / Trigonometry

QuestionSolve for $x$ . Round to the nearest tenth of a degree, if necessary.
Answer Attemptiout of 2 $x=$ $\square$ Submit Answer

Studdy Solution

STEP 1

What is this asking? We need to find the angle $x$ in a right triangle, knowing the lengths of the sides adjacent and opposite to it. Watch out! Make sure your calculator is in degree mode, and remember SOH CAH TOA!

STEP 2

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

STEP 3

Alright, let's dive into this triangle adventure!
We've got a right triangle, which means we can unleash the power of SOH CAH TOA!
We know the side adjacent to angle $x$ is $WV = 8.9$ , and the side opposite to angle $x$ is $UV = 9.8$ .

STEP 4

Which trigonometric friend should we call upon?
Since we have the opposite and adjacent sides, the tangent function is our best pal!
Remember, $\tan(x) = \frac{\text{opposite}}{\text{adjacent}}$ .

STEP 5

Let's plug in our values: $\tan(x) = \frac{9.8}{8.9}$

STEP 6

To rescue $x$ from inside the tangent function, we'll use the inverse tangent (arctan or $\tan^{-1}$ ).
It's like the superhero cape that frees our variable!

STEP 7

So, we have: $x = \tan^{-1}\left(\frac{9.8}{8.9}\right)$

STEP 8

Now, grab your calculator, make sure it's in degree mode, and punch in those numbers! $x \approx \tan^{-1}(1.1011235955)$ $x \approx 47.745^\circ$

STEP 9

The problem asks us to round to the nearest tenth, so our final answer is approximately $47.7^\circ$ .

STEP 10

$x \approx 47.7^\circ$

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QuestionSolve for $x$ . Round to the nearest tenth of a degree, if necessary.
Answer Attemptiout of 2 $x=$ $\square$ Submit Answer

Studdy Solution

STEP 1

What is this asking? We need to find the angle $x$ in a right triangle, knowing the lengths of the sides adjacent and opposite to it. Watch out! Make sure your calculator is in degree mode, and remember SOH CAH TOA!

STEP 2

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

STEP 3

Alright, let's dive into this triangle adventure!
We've got a right triangle, which means we can unleash the power of SOH CAH TOA!
We know the side adjacent to angle $x$ is $WV = 8.9$ , and the side opposite to angle $x$ is $UV = 9.8$ .

STEP 4

Which trigonometric friend should we call upon?
Since we have the opposite and adjacent sides, the tangent function is our best pal!
Remember, $\tan(x) = \frac{\text{opposite}}{\text{adjacent}}$ .

STEP 5

Let's plug in our values: $\tan(x) = \frac{9.8}{8.9}$

STEP 6

To rescue $x$ from inside the tangent function, we'll use the inverse tangent (arctan or $\tan^{-1}$ ).
It's like the superhero cape that frees our variable!

STEP 7

So, we have: $x = \tan^{-1}\left(\frac{9.8}{8.9}\right)$

STEP 8

Now, grab your calculator, make sure it's in degree mode, and punch in those numbers! $x \approx \tan^{-1}(1.1011235955)$ $x \approx 47.745^\circ$

STEP 9

The problem asks us to round to the nearest tenth, so our final answer is approximately $47.7^\circ$ .

STEP 10

$x \approx 47.7^\circ$

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QuestionSolve for xxx. Round to the nearest tenth of a degree, if necessary.Answer Attemptiout of 2 x=x=x= □\square□ Submit Answer

Studdy Solution

STEP 1

What is this asking? We need to find the angle xxx in a right triangle, knowing the lengths of the sides adjacent and opposite to it. Watch out! Make sure your calculator is in degree mode, and remember SOH CAH TOA!

STEP 2

1. Set up the trigonometric ratio2. Solve for xxx

STEP 3

Alright, let's dive into this triangle adventure!We've got a right triangle, which means we can unleash the power of SOH CAH TOA!We know the side **adjacent** to angle xxx is WV=8.9WV = 8.9WV=8.9, and the side **opposite** to angle xxx is UV=9.8UV = 9.8UV=9.8.

STEP 4

Which trigonometric friend should we call upon?Since we have the **opposite** and **adjacent** sides, the tangent function is our best pal!Remember, tan⁡(x)=oppositeadjacent\tan(x) = \frac{\text{opposite}}{\text{adjacent}}tan(x)=adjacentopposite​.

STEP 5

Let's plug in our values: tan⁡(x)=9.88.9 \tan(x) = \frac{9.8}{8.9} tan(x)=8.99.8​

STEP 6

To rescue xxx from inside the tangent function, we'll use the inverse tangent (arctan or tan⁡−1\tan^{-1}tan−1).It's like the superhero cape that frees our variable!

STEP 7

So, we have: x=tan⁡−1(9.88.9) x = \tan^{-1}\left(\frac{9.8}{8.9}\right) x=tan−1(8.99.8​)

STEP 8

Now, grab your calculator, make sure it's in degree mode, and punch in those numbers! x≈tan⁡−1(1.1011235955) x \approx \tan^{-1}(1.1011235955) x≈tan−1(1.1011235955) x≈47.745∘ x \approx 47.745^\circ x≈47.745∘

STEP 9

The problem asks us to round to the nearest tenth, so our **final answer** is approximately 47.7∘47.7^\circ47.7∘.

STEP 10

x≈47.7∘x \approx 47.7^\circx≈47.7∘

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Start learning now

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

QuestionSolve for $x$ . Round to the nearest tenth of a degree, if necessary.
Answer Attemptiout of 2 $x=$ $\square$ Submit Answer

What is this asking? We need to find the angle $x$ in a right triangle, knowing the lengths of the sides adjacent and opposite to it. Watch out! Make sure your calculator is in degree mode, and remember SOH CAH TOA!

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

Alright, let's dive into this triangle adventure!
We've got a right triangle, which means we can unleash the power of SOH CAH TOA!
We know the side adjacent to angle $x$ is $WV = 8.9$ , and the side opposite to angle $x$ is $UV = 9.8$ .

Which trigonometric friend should we call upon?
Since we have the opposite and adjacent sides, the tangent function is our best pal!
Remember, $\tan(x) = \frac{\text{opposite}}{\text{adjacent}}$ .

Let's plug in our values: $\tan(x) = \frac{9.8}{8.9}$

To rescue $x$ from inside the tangent function, we'll use the inverse tangent (arctan or $\tan^{-1}$ ).
It's like the superhero cape that frees our variable!

So, we have: $x = \tan^{-1}\left(\frac{9.8}{8.9}\right)$

Now, grab your calculator, make sure it's in degree mode, and punch in those numbers! $x \approx \tan^{-1}(1.1011235955)$ $x \approx 47.745^\circ$

The problem asks us to round to the nearest tenth, so our final answer is approximately $47.7^\circ$ .

$x \approx 47.7^\circ$