Rounded to the nearest tenth, give the value of x for the following right triangle: 56.8° 10
Rounded to the nearest tenth, give the value of x for the following right triangle: 56.8° 10
Chapter7: Rational Expressions And Functions
Section7.5: Solve Applications With Rational Equations
Problem 7.89TI: Find the actual distance from Seattle to Portland.
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![### Problem Statement:
Rounded to the nearest tenth, give the value of \( x \) for the following right triangle:
### Diagram Description:
The diagram depicts a right triangle with the following details:
- One of the angles is \( 56.8^\circ \).
- The side opposite this angle is labeled \( x \).
- The side adjacent to the \( 56.8^\circ \) angle (the base of the triangle) is labeled \( 10 \).
### Solution:
To find the value of \( x \), we can use the tangent function, which is defined as the ratio of the opposite side to the adjacent side in a right triangle. The formula is:
\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \]
Here, \( \theta = 56.8^\circ \), the opposite side is \( x \), and the adjacent side is \( 10 \).
\[ \tan(56.8^\circ) = \frac{x}{10} \]
Multiply both sides of the equation by \( 10 \) to solve for \( x \):
\[ x = 10 \times \tan(56.8^\circ) \]
Using a calculator to find \( \tan(56.8^\circ) \):
\[ \tan(56.8^\circ) \approx 1.5161 \]
Thus,
\[ x \approx 10 \times 1.5161 \approx 15.161 \]
Rounded to the nearest tenth:
\[ x \approx 15.2 \]
Therefore, the value of \( x \) is approximately \( 15.2 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd24861ef-92b0-4cd8-8c54-2ac2200498ec%2Fef0b485a-05d4-4978-bafa-1622cd388837%2F881ixv_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem Statement:
Rounded to the nearest tenth, give the value of \( x \) for the following right triangle:
### Diagram Description:
The diagram depicts a right triangle with the following details:
- One of the angles is \( 56.8^\circ \).
- The side opposite this angle is labeled \( x \).
- The side adjacent to the \( 56.8^\circ \) angle (the base of the triangle) is labeled \( 10 \).
### Solution:
To find the value of \( x \), we can use the tangent function, which is defined as the ratio of the opposite side to the adjacent side in a right triangle. The formula is:
\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \]
Here, \( \theta = 56.8^\circ \), the opposite side is \( x \), and the adjacent side is \( 10 \).
\[ \tan(56.8^\circ) = \frac{x}{10} \]
Multiply both sides of the equation by \( 10 \) to solve for \( x \):
\[ x = 10 \times \tan(56.8^\circ) \]
Using a calculator to find \( \tan(56.8^\circ) \):
\[ \tan(56.8^\circ) \approx 1.5161 \]
Thus,
\[ x \approx 10 \times 1.5161 \approx 15.161 \]
Rounded to the nearest tenth:
\[ x \approx 15.2 \]
Therefore, the value of \( x \) is approximately \( 15.2 \).
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