The problem shows a right triangle with sides measuring 230 m, 90 m, and an angle labeled as $x^\circ$. To solve for $x$, we can use trigonometric relations, specifically the tangent function, because we have the opposite and adjacent sides relative to angle $x$.

Given:

• Opposite side = 90 m
• Adjacent side = 230 m

We can use the formula for tangent: $\tan(x) = \frac{\text{opposite}}{\text{adjacent}} = \frac{90}{230}$

Now, we calculate the value of $\tan(x)$: $\tan(x) = \frac{90}{230} \approx 0.3913$

To find the angle $x$, we take the inverse tangent (arctan) of 0.3913: $x = \tan^{-1}(0.3913)$

Using a calculator: $x \approx 21.4^\circ$

Thus, $x \approx 21.4^\circ$.

Would you like more details on the solution or have any other questions? Here are some related questions to explore further:

1. How can you use the sine or cosine functions to solve for the angle instead of tangent?
2. What are the basic trigonometric ratios, and when are they applied in right triangles?
3. How would you calculate the hypotenuse of a right triangle if you know the other two sides?
4. How can you apply the Pythagorean Theorem to check the sides of a triangle?
5. What are some real-life applications of trigonometry in fields like navigation or construction?

Tip: When dealing with right triangles, always identify which sides (opposite, adjacent, and hypotenuse) relate to the angle in question, as this will guide you to the correct trigonometric function to use.