Answer:
a = 4
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
- Multiplication Property of Equality
- Division Property of Equality
- Addition Property of Equality
- Subtraction Property of Equality
<u>Trigonometry</u>
[Right Triangles Only] Pythagorean Theorem: a² + b² = c²
- a is a leg
- b is another leg
- c is the hypotenuse<u>
</u>
Step-by-step explanation:
<u>Step 1: Define</u>
Leg <em>a</em> = <em>a</em>
Leg <em>b</em> = 3
Hypotenuse <em>c</em> = 5
<u>Step 2: Solve for </u><em><u>a</u></em>
- Substitute in variables [Pythagorean Theorem]: a² + 3² = 5²
- [Subtraction Property of Equality] Isolate <em>a </em>term: a² = 5² - 3²
- Evaluate exponents: a² = 25 - 9
- Subtract: a² = 16
- [Equality Property] Isolate <em>a</em>: a = ±4
Since we are dealing with a regular right triangle and not a quadrant triangle, we use the positive root.
∴ a = 4