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The image you uploaded is of a triangle where you need to determine the tangent of angle \( \theta \). This triangle is not a standard right triangle; it involves algebraic expressions for its sides. 

Firstly, notice that the sum of the angles in any triangle is 180°. Therefore, angle \( \theta \) is the supplement of 30°, so \( \theta = 150° \).

The tangent of 150° can be calculated using the tangent subtraction identity:
\[
\tan(150^\circ) = \tan(180^\circ - 30^\circ) = -\tan(30^\circ)
\]

The value of \( \tan(30^\circ) \) is well-known:
\[
\tan(30^\circ) = \frac{1}{\sqrt{3}}
\]

Thus:
\[
\tan(150^\circ) = -\frac{1}{\sqrt{3}}
\]

Do you want details about the tangent subtraction identity or have any other questions? Here are some additional related queries you might consider:

1. How do you derive the tangent subtraction identity?
2. What are the tangent values for other common angles?
3. How would you solve for \( x \) if more information is given about the sides of the triangle?
4. How does the tangent function behave in different quadrants?
5. Can you explain why the sum of angles in a triangle always equals 180°?

**Tip:** When dealing with trigonometry involving unknown angles, always check if your angle might be in a different quadrant, as this affects the sign of the trigonometric function values.

Determine tg(θ) based on the given triangle with sides labeled as algebraic expressions.

Learn how to determine the tangent of an angle θ in a triangle where sides are given as algebraic expressions. This problem covers trigonometric concepts and uses the tangent subtraction identity. Suitable for students in Grades 10-12.

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