Question

Find the third side in simplest radical form:

Answer 1

x = √53

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

1. Brackets
2. Parenthesis
3. Exponents
4. Multiplication
5. Division
6. Addition
7. Subtraction

• Left to Right

Equality Properties

Trigonometry

• [Right Triangles Only] Pythagorean Theorem: a² + b² = c²

Explanation:

Step 1: Define

We are given a right triangle. We can use PT to solve for the missing length.

Step 2: Identify Variables

Leg a = 6

Leg b = x

Hypotenuse c = √89

Step 3: Solve for x

1. Set up equation: 6² + x² = (√89)²
2. Isolate x term: x² = (√89)² - 6²
3. Exponents: x² = 89 - 36
4. Subtract: x² = 53
5. Isolate x: x = √53