Find the value of the angle theta in degrees rounded to the nearest tenth of a degree.
theta
9
36
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Part 1
thetaequals
  
enter your response heredegrees ​(Round to one decimal place as​ needed.)

It seems like you have a triangle or trigonometric problem involving an angle \(\theta\) and possibly two side lengths (9 and 36). Let's proceed by determining how these values relate to the angle.

If the triangle is a right triangle, we can use trigonometric functions like sine, cosine, or tangent to find the angle \(\theta\). For example:

- If the given values (9 and 36) represent the opposite and adjacent sides, you could use the tangent function:
  \[
  \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{9}{36} = 0.25
  \]
  To find \(\theta\), take the inverse tangent:
  \[
  \theta = \tan^{-1}(0.25)
  \]
  
Let's compute this value.

The value of the angle \(\theta\) is approximately \(14.0^\circ\) when rounded to the nearest tenth of a degree.

Would you like more details on this or have any questions?

Here are 5 related questions to expand on this topic:
1. How do you use sine, cosine, and tangent to find angles in a right triangle?
2. What is the relationship between the sides and angles of a right triangle?
3. How can we solve for unknown sides if we know one angle and one side in a right triangle?
4. What are the key differences between the sine, cosine, and tangent functions?
5. How do you convert between radians and degrees?

**Tip:** The tangent of an angle in a right triangle is the ratio of the opposite side to the adjacent side.

Find the value of the angle theta in degrees rounded to the nearest tenth of a degree.

Discover how to calculate the angle theta in a right triangle using the tangent function. This step-by-step guide explains the trigonometric ratio and how to apply the inverse tangent function to find theta, suitable for students in Grades 9-12.

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