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This is a right triangle where you are asked to find the value of \( x \), given that \( a = 53 \) and using the angles \( 56^\circ \) and \( 39^\circ \).

To solve for \( x \), we can use the law of sines, which relates the sides of a triangle to the sines of their opposite angles:

\[
\frac{a}{\sin(39^\circ)} = \frac{x}{\sin(56^\circ)}
\]

Given:
- \( a = 53 \)
- \( \sin(39^\circ) \) and \( \sin(56^\circ) \) are the sines of the given angles.

Let's compute \( x \) using this formula.The value of \( x \) is approximately \( 69.82 \), rounded to the nearest hundredth.

Would you like more details or have any questions?

Here are 5 related questions you might find useful:
1. How would you solve for the other sides if the triangle was not a right triangle?
2. Can you find the third side of the triangle using the Pythagorean theorem?
3. What other trigonometric laws can be applied to non-right triangles?
4. How does the law of sines differ from the law of cosines?
5. Can you derive the law of sines from basic trigonometric principles?

**Tip:** Always check if the angles and sides correspond to known trigonometric laws to simplify solving triangle problems.

Find the length of x in a right triangle with angles 56° and 39°, given that side a = 53.

Learn how to find the length of side x in a right triangle with angles 56° and 39°, given that side a = 53. This example uses the Law of Sines and trigonometric identities. Suitable for high school students.

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