https://file.aiquickdraw.com/mathbot/file/1726250893091babj260i.jpg

The problem shows a right triangle with angles of 30° and 60°, and the hypotenuse is 89 units. You are asked to find the length of \(x\), the side opposite the 30° angle, rounded to one decimal place.

### Using the properties of a 30°-60°-90° triangle:
- The side opposite the 30° angle is half the length of the hypotenuse.
- The side opposite the 60° angle is \( \sqrt{3}/2 \) times the hypotenuse.

Therefore:
- \( x = \frac{1}{2} \times 89 = 44.5 \)

Thus, \( x = 44.5 \).

Would you like further details or have any questions?

Here are 5 related questions:
1. How can I find the side opposite the 60° angle?
2. What are the properties of a 30°-60°-90° triangle?
3. How can I use trigonometric ratios (like sine and cosine) to solve for side lengths?
4. How do I apply the Pythagorean theorem to verify the side lengths?
5. Why are the ratios in a 30°-60°-90° triangle constant?

**Tip:** In special triangles, such as the 30°-60°-90° triangle, the side lengths are always proportional to each other, making calculations simpler.

Find x rounded to one decimal place in a 30°-60°-90° triangle with a hypotenuse of 89 units.

Learn how to find the side length of x in a 30°-60°-90° triangle with a hypotenuse of 89 units, using the properties of special right triangles. This step-by-step guide covers key trigonometric concepts and formulas, suitable for Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation