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Solve for x.  Round to two decimal places, if necessary

The image you uploaded depicts a right triangle where:
- The hypotenuse is 11 meters.
- One of the angles is \( 34^\circ \).
- The side opposite this angle is \( x \), which we need to solve for.

To solve for \( x \), we can use the sine function from trigonometry because the sine of an angle in a right triangle is the ratio of the opposite side to the hypotenuse:

\[
\sin(34^\circ) = \frac{x}{11}
\]

Now, solve for \( x \):

\[
x = 11 \times \sin(34^\circ)
\]

I will now calculate the value of \( x \).The length of \( x \) is approximately 6.15 meters when rounded to two decimal places.

Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:
1. How would you find the adjacent side using the given information?
2. What trigonometric function would you use to find the angle if the opposite and adjacent sides were known?
3. If the angle was changed to 45°, how would the length of \( x \) be affected?
4. How do we calculate the area of this right triangle given the values of the sides?
5. Can the Pythagorean theorem be used to solve for \( x \)? Why or why not?

**Tip:** Always verify whether the angle you're using is opposite or adjacent to the side you're solving for to choose the correct trigonometric function.

Solve for x. Round to two decimal places, if necessary.

Learn how to solve for x in a right triangle with a 34° angle and 11m hypotenuse. This trigonometry problem demonstrates how to use sine function to find the opposite side. Suitable for students in Grades 9-11.

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