The problem you've uploaded seems to involve solving for the side $x$ in a right triangle where the lengths of one side and the angle are provided. Let's break down the information:

• The angle at $\angle C = 70^\circ$.
• One side of the triangle, $BC = 8$ (adjacent to angle $70^\circ$).
• The side $x$ is opposite angle $70^\circ$.

We can use the tangent function from trigonometry, which relates the opposite side to the adjacent side:

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

Substituting the values:

$\tan(70^\circ) = \frac{x}{8}.$

Now, solve for $x$:

$x = 8 \cdot \tan(70^\circ).$

Next, we can calculate the value of $x$ by finding $\tan(70^\circ)$ and multiplying by 8.

Let me do the calculation for you. math

Given values

angle = 70 # degrees adjacent = 8 # side BC

Convert angle to radians for calculation

angle_radians = math.radians(angle)

Calculate x using the tangent function

x = adjacent * math.tan(angle_radians) x_rounded = round(x, 1)

x_roundedThe value of $x$ is approximately 22.0, rounded to the nearest tenth.

If you have any further questions or need more details, feel free to ask!

Here are 5 follow-up questions to expand on the concept:

1. What other trigonometric functions can be used to solve for unknown sides in right triangles?
2. How can you use the sine and cosine functions in this type of problem?
3. What happens if the angle in the triangle changes, how does it affect $x$?
4. Can the Law of Sines or Law of Cosines be applied to this type of triangle?
5. What is the general process for solving for unknown sides in right triangles?

Tip: Always make sure to convert the angle to radians if your calculator or software is set to use radians for trigonometric calculations!