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To solve for the angle \(\theta\) in the given right triangle, we can use the tangent function. The tangent of an angle in a right triangle is the ratio of the length of the opposite side to the length of the adjacent side. Here, the opposite side to angle \(\theta\) is 14 cm, and the adjacent side is 9 cm.

The formula for tangent is:
\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \]

Substitute the given values:
\[ \tan(\theta) = \frac{14}{9} \]

Now, to find \(\theta\), we take the arctangent (inverse tangent) of \(\frac{14}{9}\):
\[ \theta = \tan^{-1}\left(\frac{14}{9}\right) \]

Using a calculator to find the arctangent:
\[ \theta \approx \tan^{-1}(1.5556) \]
\[ \theta \approx 57.99^\circ \]

Rounding to the nearest integer:
\[ \theta \approx 58^\circ \]

So, the size of angle \(\theta\) is approximately \(58^\circ\).

Would you like any additional details or have any questions?

Here are some related questions:
1. How do you use the sine function to find the hypotenuse in a right triangle?
2. What is the relationship between the angles in a right triangle?
3. How can the Pythagorean theorem be used to find the length of the hypotenuse?
4. What are the definitions of the sine and cosine functions in a right triangle?
5. How can you convert degrees to radians?

**Tip:** Always ensure your calculator is set to the correct mode (degrees or radians) depending on the unit you need for your angle measurements.

By first finding tan θ, calculate the size of angle θ. Give your answer in degrees to the nearest integer. The triangle has opposite side = 14 cm and adjacent side = 9 cm.

Learn how to calculate the size of angle θ in a right triangle using the tangent function. With opposite side = 14 cm and adjacent side = 9 cm, we use tan(θ) = opposite/adjacent and the arctangent function to find θ ≈ 58°. Step-by-step explanation included for students in Grades 9-10.

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