Special right triangle with one angle being 45 and one side being 5 find missing sidez

For a **special right triangle** where one angle is **45°**, we are dealing with a **45°-45°-90° triangle**. This is an **isosceles right triangle**, meaning the two legs are equal in length, and the ratio of the sides follows a specific pattern.

In a **45°-45°-90° triangle**:
- The two legs are congruent.
- The hypotenuse is \( \sqrt{2} \) times the length of either leg.

If you know one side, say the **leg**, and its value is 5, we can find the hypotenuse using the ratio:
\[
\text{Hypotenuse} = \text{Leg} \times \sqrt{2}
\]
So, if the leg is 5:
\[
\text{Hypotenuse} = 5 \times \sqrt{2} = 5\sqrt{2} \approx 7.071
\]

If the given side is the **hypotenuse**, we can solve for the legs using:
\[
\text{Leg} = \frac{\text{Hypotenuse}}{\sqrt{2}}
\]
For example, if the hypotenuse is 5:
\[
\text{Leg} = \frac{5}{\sqrt{2}} = \frac{5\sqrt{2}}{2} \approx 3.535
\]

Do you want to specify which side is 5, the leg or the hypotenuse, so I can help calculate the missing side more precisely?

---

**Related Questions:**
1. How do you solve for the hypotenuse of a 30°-60°-90° triangle?
2. What is the general formula for the sides of a 45°-45°-90° triangle?
3. How do you calculate the area of a 45°-45°-90° triangle?
4. What is the relationship between the angles and side lengths in a right triangle?
5. How do you determine the type of right triangle based on the side lengths?

**Tip:** When working with special right triangles, always remember the exact ratios—45°-45°-90° triangles have leg-to-hypotenuse ratios involving \( \sqrt{2} \), and 30°-60°-90° triangles have leg-to-hypotenuse ratios involving \( \sqrt{3} \).

Learn how to solve for the missing side of a 45°-45°-90° triangle when one side is given. This guide covers the specific ratios and formulas for isosceles right triangles, including the relationship between legs and hypotenuse. Ideal for students in Grades 7-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation