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We have a right triangle with a known side length of 115 units and two angles given as 56° and 35°. The goal is to find \(x\), which is the length of the base (the side adjacent to the 35° angle).

To solve for \(x\), we can use trigonometric relationships. Specifically, we will apply the sine rule (Law of Sines) or trigonometric functions, since we know an angle and the length of the hypotenuse (115 units).

Using the Law of Sines:
\[
\frac{\sin(35^\circ)}{115} = \frac{\sin(56^\circ)}{x}
\]

Now let's solve for \(x\). I will calculate this.The length of \( x \), the base of the triangle, is approximately 166.22 units.

Would you like more details or clarifications on any part of this solution?

Here are 5 related questions that you might find interesting:
1. How would you use the cosine rule to solve a triangle?
2. What if the given angle was 90°, how would the solution change?
3. How can you find the height of the triangle using the angles provided?
4. What if you only knew two sides of the triangle? How would you find the angles?
5. Can you solve this problem using the Law of Cosines instead?

**Tip:** Always check if you can use basic trigonometric functions (sine, cosine, tangent) in a right triangle to simplify calculations.

Find the value of x in the right triangle with angles 56° and 35°, and a known hypotenuse of 115 units.

Learn how to solve for x in a right triangle using trigonometric relationships. The problem involves angles of 56° and 35°, and a known hypotenuse of 115 units. Discover the Law of Sines and trigonometric ratios in this step-by-step solution.

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