
Homework:9.1 HW - Applications Involving Right Triangles
Question 25, 9.1.45
HW Score: 96%, 24 of 25 points
 Points: 0 of 1


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Part 1
Find the value of the angle theta in degrees rounded to the nearest tenth of a degree.
theta
6
24
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Part 1
thetaequals
  
enter your response heredegrees ​(Round to one decimal place as​ needed.)
input field 1(Round to one decimal place as needed.)input field 1(Round to one decimal place as needed.)
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To find the angle \( \theta \) in a right triangle where the side opposite \( \theta \) is \( 6 \) and the side adjacent to \( \theta \) is \( 24 \), you can use the tangent function:

\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{6}{24}
\]

### Step 1: Calculate the Tangent Ratio
\[
\tan(\theta) = \frac{6}{24} = 0.25
\]

### Step 2: Find \( \theta \) Using the Inverse Tangent
Now, take the inverse tangent (arctan) of \( 0.25 \) to find \( \theta \):
\[
\theta = \arctan(0.25)
\]

Using a calculator:
\[
\theta \approx 14.0^\circ
\]

### Answer:
\[
\theta \approx 14.0^\circ
\]

Let me know if you'd like more details or have questions. Here are related problems you might find useful:

1. How would you find \( \theta \) if you were given the hypotenuse and the opposite side?
2. What is the angle \( \theta \) if the sides are scaled by a factor?
3. How would you find the adjacent side if given \( \theta \) and the opposite side?
4. What happens to \( \theta \) if the opposite side is doubled?
5. Can you solve for \( \theta \) using cosine if both the adjacent and hypotenuse are known?

**Tip:** When using trigonometric ratios, remember which sides correspond to opposite, adjacent, and hypotenuse relative to the angle you’re calculating.

Find the value of the angle theta in degrees rounded to the nearest tenth of a degree. Given opposite side = 6 and adjacent side = 24.

Learn how to find the angle theta in a right triangle given the opposite side of 6 and adjacent side of 24. This problem illustrates the use of the tangent function and inverse tangent to determine angles. Suitable for students in Grades 8-10.

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