https://r2.erweima.ai/mathbot/image/17264186715580vfub62y.jpg

The problem in the image asks to calculate the angle in sexagesimal degrees (°) given two equations related to sine (S) and cosine (C):

1. \( S = 3(x + 30) \)
2. \( C = 8(x + 9) \)

It looks like these equations are related to solving for an angle \( x \). Here's how we can proceed to solve this:

### Step 1: Use the relation between sine and cosine.
The general identity that relates sine and cosine for an angle \( x \) is:
\[
\tan(x) = \frac{\sin(x)}{\cos(x)}
\]
Here, \( S \) and \( C \) might represent the sine and cosine of an angle after being multiplied by some constants. To extract \( x \), we need to divide the expressions for \( S \) and \( C \):

\[
\frac{S}{C} = \frac{3(x + 30)}{8(x + 9)}
\]
This will help us solve for \( x \) by isolating the variable.

### Step 2: Solve for \( x \).

We can simplify the equation to:

\[
\frac{3(x + 30)}{8(x + 9)} = \tan(\theta)
\]
where \( \theta \) is the angle we are looking for. You can solve this equation numerically for \( x \), and then determine the angle \( \theta \) using the inverse tangent function.

Would you like to proceed with solving for \( x \) and calculating the angle? Let me know if you'd like further details on any specific part! 

### Related Questions:
1. How do you solve a system of equations involving trigonometric functions?
2. What is the relationship between sine and cosine in trigonometry?
3. Can we solve for \( x \) using another trigonometric identity?
4. How do we convert radians to degrees if needed?
5. How does the tangent function work for angles?

### Tip:
When solving trigonometric equations, always check the periodicity of the functions since multiple solutions might exist depending on the range of angles you're working with.

Calcula el ángulo sexagesimal que cumple: S = 3(x + 30), C = 8(x + 9)

Learn how to calculate the angle θ in degrees using trigonometric equations for sine (S = 3(x + 30)) and cosine (C = 8(x + 9)). This problem covers key trigonometric concepts and algebraic manipulation. Suitable for high school students in Grades 9-12.

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