Question

Find the length of the hypotenuse.

12
5
18
6

Answer 1

6

Explanation:

sin 45° = 3√2/ h

h = 3√2/ sin 45°

= 6

Answer 2

6

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] SOHCAHTOA
• [Right Triangles Only] sinθ = opposite over hypotenuse

Explanation:

Step 1: Define

Identify variables

Angle θ = 45°

Opposite Leg: 3√2

Step 2: Find Hypotenuse

1. Substitute in variables [Sine]:
   `\displaystyle sin(45^\circ) = (3√(2))/(c)`
2. [Multiplication Property of Equality] Cross-multiply:
   `\displaystyle c = (3√(2))/(sin(45^\circ))`
3. Evaluate:
   `\displaystyle c = 6`