To solve for $x$ in the given right triangle, we can use trigonometric ratios. Specifically, since we have the angle $35^\circ$, the adjacent side (15), and we are solving for the opposite side ($x$), we use the tangent function:

$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$

Substituting the given values:

$\tan(35^\circ) = \frac{x}{15}$

Solving for $x$:

$x = 15 \cdot \tan(35^\circ)$

Let me calculate this. math

Given values

angle = 35 # in degrees adjacent = 15 # length of adjacent side

Calculate the opposite side (x)

x = adjacent * math.tan(math.radians(angle)) xThe value of $x$ is approximately $10.5$ (rounded to the nearest tenth).

Would you like further clarification or detailed steps? Here are some related questions for practice:

1. How would the calculation change if the angle was $45^\circ$?
2. Can you solve for the hypotenuse of this triangle?
3. How would you use the sine function to find $x$?
4. What is the area of the triangle with the given values?
5. How does the tangent ratio change as the angle increases?

Tip: Always make sure your calculator is set to degrees (not radians) when working with angles in degrees.