Math / Geometry

QuestionFind QS.
Write your answer as an integer or as a decimal rounded to the nearest tenth. $Q S=$ $\square$

Studdy Solution

STEP 1

What is this asking? We're looking for the length of a side in a right triangle, knowing one side and an angle! 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 QS

STEP 3

Alright, we've got a right triangle, a known side, and an angle.
This screams trigonometry!
We're trying to find $QS$ , which is adjacent to the $29^\circ$ angle, and we know $RQ$ , which is opposite to the $29^\circ$ angle.

STEP 4

Which trigonometric function relates the opposite and adjacent sides?
It's the tangent function!
Remember SOH CAH TOA.
TOA stands for Tangent is Opposite over Adjacent.

STEP 5

So, we can write: $\tan(29^\circ) = \frac{\text{opposite}}{\text{adjacent}} = \frac{RQ}{QS} = \frac{3.9}{QS}$

STEP 6

Our goal is to isolate $QS$ .
To do this, we can multiply both sides of the equation by $QS$ : $QS \cdot \tan(29^\circ) = 3.9$

STEP 7

Now, divide both sides by $\tan(29^\circ)$ to get $QS$ by itself: $QS = \frac{3.9}{\tan(29^\circ)}$

STEP 8

Time to grab our calculator!
Make sure it's in degree mode.
We calculate $\tan(29^\circ)$ which is approximately 0.5543.

STEP 9

Now, we divide $3.9$ by 0.5543: $QS = \frac{3.9}{0.5543} \approx 7.0$

STEP 10

$QS \approx 7.0$

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QuestionFind QS.
Write your answer as an integer or as a decimal rounded to the nearest tenth. $Q S=$ $\square$

Studdy Solution

STEP 1

What is this asking? We're looking for the length of a side in a right triangle, knowing one side and an angle! 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 QS

STEP 3

Alright, we've got a right triangle, a known side, and an angle.
This screams trigonometry!
We're trying to find $QS$ , which is adjacent to the $29^\circ$ angle, and we know $RQ$ , which is opposite to the $29^\circ$ angle.

STEP 4

Which trigonometric function relates the opposite and adjacent sides?
It's the tangent function!
Remember SOH CAH TOA.
TOA stands for Tangent is Opposite over Adjacent.

STEP 5

So, we can write: $\tan(29^\circ) = \frac{\text{opposite}}{\text{adjacent}} = \frac{RQ}{QS} = \frac{3.9}{QS}$

STEP 6

Our goal is to isolate $QS$ .
To do this, we can multiply both sides of the equation by $QS$ : $QS \cdot \tan(29^\circ) = 3.9$

STEP 7

Now, divide both sides by $\tan(29^\circ)$ to get $QS$ by itself: $QS = \frac{3.9}{\tan(29^\circ)}$

STEP 8

Time to grab our calculator!
Make sure it's in degree mode.
We calculate $\tan(29^\circ)$ which is approximately 0.5543.

STEP 9

Now, we divide $3.9$ by 0.5543: $QS = \frac{3.9}{0.5543} \approx 7.0$

STEP 10

$QS \approx 7.0$

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QuestionFind QS.Write your answer as an integer or as a decimal rounded to the nearest tenth. QS=Q S=QS= □\square□

Studdy Solution

STEP 1

What is this asking? We're looking for the length of a side in a right triangle, knowing one side and an angle! Watch out! Make sure your calculator is in degree mode, not radians!Also, remember SOH CAH TOA.

STEP 2

1. Set up the trigonometric ratio2. Solve for QS

STEP 3

Alright, we've got a right triangle, a known side, and an angle.This screams trigonometry!We're trying to find QSQSQS, which is adjacent to the **29∘29^\circ29∘ angle**, and we know RQRQRQ, which is **opposite** to the 29∘29^\circ29∘ angle.

STEP 4

Which trigonometric function relates the opposite and adjacent sides?It's the **tangent** function!Remember SOH CAH TOA.TOA stands for Tangent is Opposite over Adjacent.

STEP 5

So, we can write: tan⁡(29∘)=oppositeadjacent=RQQS=3.9QS\tan(29^\circ) = \frac{\text{opposite}}{\text{adjacent}} = \frac{RQ}{QS} = \frac{3.9}{QS}tan(29∘)=adjacentopposite​=QSRQ​=QS3.9​

STEP 6

Our goal is to isolate QSQSQS.To do this, we can multiply both sides of the equation by QSQSQS: QS⋅tan⁡(29∘)=3.9QS \cdot \tan(29^\circ) = 3.9QS⋅tan(29∘)=3.9

STEP 7

Now, divide both sides by tan⁡(29∘)\tan(29^\circ)tan(29∘) to get QSQSQS by itself: QS=3.9tan⁡(29∘)QS = \frac{3.9}{\tan(29^\circ)}QS=tan(29∘)3.9​

STEP 8

Time to grab our calculator!Make sure it's in degree mode.We calculate tan⁡(29∘)\tan(29^\circ)tan(29∘) which is approximately **0.5543**.

STEP 9

Now, we divide 3.93.93.9 by **0.5543**: QS=3.90.5543≈7.0QS = \frac{3.9}{0.5543} \approx 7.0QS=0.55433.9​≈7.0

STEP 10

QS≈7.0QS \approx 7.0QS≈7.0

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QuestionFind QS.
Write your answer as an integer or as a decimal rounded to the nearest tenth. $Q S=$ $\square$

What is this asking? We're looking for the length of a side in a right triangle, knowing one side and an angle! Watch out! Make sure your calculator is in degree mode, not radians!
Also, remember SOH CAH TOA.

1. Set up the trigonometric ratio
2. Solve for QS

Alright, we've got a right triangle, a known side, and an angle.
This screams trigonometry!
We're trying to find $QS$ , which is adjacent to the $29^\circ$ angle, and we know $RQ$ , which is opposite to the $29^\circ$ angle.

Which trigonometric function relates the opposite and adjacent sides?
It's the tangent function!
Remember SOH CAH TOA.
TOA stands for Tangent is Opposite over Adjacent.

So, we can write: $\tan(29^\circ) = \frac{\text{opposite}}{\text{adjacent}} = \frac{RQ}{QS} = \frac{3.9}{QS}$

Our goal is to isolate $QS$ .
To do this, we can multiply both sides of the equation by $QS$ : $QS \cdot \tan(29^\circ) = 3.9$

Now, divide both sides by $\tan(29^\circ)$ to get $QS$ by itself: $QS = \frac{3.9}{\tan(29^\circ)}$

Time to grab our calculator!
Make sure it's in degree mode.
We calculate $\tan(29^\circ)$ which is approximately 0.5543.

Now, we divide $3.9$ by 0.5543: $QS = \frac{3.9}{0.5543} \approx 7.0$

$QS \approx 7.0$