Question

A right triangle has leg lengths 4.5 and 4.5^3 what are the measures of the angles

Answer 1

The triangle is identified as a 30°-60°-90° special right triangle because the long leg is √3 times the short leg. The angles are 30, 60, and 90 degrees.

Let's break down the steps to show why the triangle is considered a 30°-60°-90° special right triangle:

1. Given Information:

- The long leg is
`\(√(3)\)` times the short leg.

2. Ratio in a 30°-60°-90° Triangle:

- In a 30°-60°-90° triangle, the sides have a specific ratio: short leg

`(\(1\)) : long leg (\(√(3)\))` : hypotenuse (2).

- The given information aligns with the ratio of a 30°-60°-90° triangle.

3. Identify the Angles:

- In this special triangle, the angles are precisely 30 degrees, 60 degrees, and 90 degrees.

4. Conclusion:

- Based on the given condition that the long leg is
`\(√(3)\)` times the short leg, we can conclude that the triangle is a 30°-60°-90° special right triangle.

5. Measures of the Angles:

- Therefore, the measures of the angles are 30 degrees, 60 degrees, and 90 degrees.