Question

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Answer 1

a = 4

Explanation:

a^2 + b^2 = c^2

a= ?

b= 3

c= 5 (c is always the hypotenuse)

*plug in given values

a^2 + 3^2 = 5^2

a^2 + 9 = 25

-9 -9

a^2 = 16

*find the square root

sqrt(a) = sqrt(16)

a = 4

Answer 2

a = 4

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

• Multiplication Property of Equality
• Division Property of Equality
• Addition Property of Equality
• Subtraction Property of Equality

Trigonometry

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

• a is a leg
• b is another leg
• c is the hypotenuse

Explanation:

Step 1: Define

Leg a = a

Leg b = 3

Hypotenuse c = 5

Step 2: Solve for a

1. Substitute in variables [Pythagorean Theorem]: a² + 3² = 5²
2. [Subtraction Property of Equality] Isolate a term: a² = 5² - 3²
3. Evaluate exponents: a² = 25 - 9
4. Subtract: a² = 16
5. [Equality Property] Isolate a: a = ±4

Since we are dealing with a regular right triangle and not a quadrant triangle, we use the positive root.

∴ a = 4