Math / Trigonometry

QuestionSolve for $x$ . Round to the nearest tenth of a degree, if necessary.

Studdy Solution

STEP 1

1. The triangle $\triangle IJK$ is a right triangle with a right angle at $J$ .
2. The side $IJ$ is the side adjacent to angle $x$ .
3. The hypotenuse $IK$ is opposite the right angle.
4. We need to find the angle $x$ using trigonometric ratios.

STEP 2

1. Identify the appropriate trigonometric function.
2. Set up the equation using the trigonometric function.
3. Solve for $x$ .
4. Round $x$ to the nearest tenth of a degree.

STEP 3

Identify the appropriate trigonometric function:
Since we have the adjacent side ( $IJ = 23$ ) and the hypotenuse ( $IK = 53$ ), we use the cosine function:
$\cos(x) = \frac{\text{Adjacent}}{\text{Hypotenuse}}$

STEP 4

Set up the equation using the cosine function:
$\cos(x) = \frac{23}{53}$

STEP 5

Solve for $x$ by taking the inverse cosine:
$x = \cos^{-1}\left(\frac{23}{53}\right)$

STEP 6

Calculate $x$ and round to the nearest tenth of a degree:
Using a calculator, find:
$x \approx \cos^{-1}\left(\frac{23}{53}\right) \approx 65.4^\circ$
The value of $x$ is:
$\boxed{65.4^\circ}$

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QuestionSolve for $x$ . Round to the nearest tenth of a degree, if necessary.

Studdy Solution

STEP 1

1. The triangle $\triangle IJK$ is a right triangle with a right angle at $J$ .
2. The side $IJ$ is the side adjacent to angle $x$ .
3. The hypotenuse $IK$ is opposite the right angle.
4. We need to find the angle $x$ using trigonometric ratios.

STEP 2

1. Identify the appropriate trigonometric function.
2. Set up the equation using the trigonometric function.
3. Solve for $x$ .
4. Round $x$ to the nearest tenth of a degree.

STEP 3

Identify the appropriate trigonometric function:
Since we have the adjacent side ( $IJ = 23$ ) and the hypotenuse ( $IK = 53$ ), we use the cosine function:
$\cos(x) = \frac{\text{Adjacent}}{\text{Hypotenuse}}$

STEP 4

Set up the equation using the cosine function:
$\cos(x) = \frac{23}{53}$

STEP 5

Solve for $x$ by taking the inverse cosine:
$x = \cos^{-1}\left(\frac{23}{53}\right)$

STEP 6

Calculate $x$ and round to the nearest tenth of a degree:
Using a calculator, find:
$x \approx \cos^{-1}\left(\frac{23}{53}\right) \approx 65.4^\circ$
The value of $x$ is:
$\boxed{65.4^\circ}$

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QuestionSolve for xxx. Round to the nearest tenth of a degree, if necessary.

Studdy Solution

STEP 1

1. The triangle △IJK \triangle IJK △IJK is a right triangle with a right angle at J J J.2. The side IJ IJ IJ is the side adjacent to angle x x x.3. The hypotenuse IK IK IK is opposite the right angle.4. We need to find the angle x x x using trigonometric ratios.

STEP 2

1. Identify the appropriate trigonometric function.2. Set up the equation using the trigonometric function.3. Solve for x x x.4. Round x x x to the nearest tenth of a degree.

STEP 3

Identify the appropriate trigonometric function:Since we have the adjacent side (IJ=23 IJ = 23 IJ=23) and the hypotenuse (IK=53 IK = 53 IK=53), we use the cosine function:cos⁡(x)=AdjacentHypotenuse \cos(x) = \frac{\text{Adjacent}}{\text{Hypotenuse}} cos(x)=HypotenuseAdjacent​

STEP 4

Set up the equation using the cosine function:cos⁡(x)=2353 \cos(x) = \frac{23}{53} cos(x)=5323​

STEP 5

Solve for x x x by taking the inverse cosine:x=cos⁡−1(2353) x = \cos^{-1}\left(\frac{23}{53}\right) x=cos−1(5323​)

STEP 6

Calculate x x x and round to the nearest tenth of a degree:Using a calculator, find:x≈cos⁡−1(2353)≈65.4∘ x \approx \cos^{-1}\left(\frac{23}{53}\right) \approx 65.4^\circ x≈cos−1(5323​)≈65.4∘ The value of x x x is:65.4∘ \boxed{65.4^\circ} 65.4∘​

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QuestionSolve for $x$ . Round to the nearest tenth of a degree, if necessary.

1. The triangle $\triangle IJK$ is a right triangle with a right angle at $J$ .
2. The side $IJ$ is the side adjacent to angle $x$ .
3. The hypotenuse $IK$ is opposite the right angle.
4. We need to find the angle $x$ using trigonometric ratios.

1. Identify the appropriate trigonometric function.
2. Set up the equation using the trigonometric function.
3. Solve for $x$ .
4. Round $x$ to the nearest tenth of a degree.

Identify the appropriate trigonometric function:
Since we have the adjacent side ( $IJ = 23$ ) and the hypotenuse ( $IK = 53$ ), we use the cosine function:
$\cos(x) = \frac{\text{Adjacent}}{\text{Hypotenuse}}$

Set up the equation using the cosine function:
$\cos(x) = \frac{23}{53}$

Solve for $x$ by taking the inverse cosine:
$x = \cos^{-1}\left(\frac{23}{53}\right)$

Calculate $x$ and round to the nearest tenth of a degree:
Using a calculator, find:
$x \approx \cos^{-1}\left(\frac{23}{53}\right) \approx 65.4^\circ$
The value of $x$ is:
$\boxed{65.4^\circ}$