Answer: The answer is 64 inches
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Answer:
![\displaystyle cos\theta = \frac{2\sqrt{13}}{13}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20cos%5Ctheta%20%3D%20%5Cfrac%7B2%5Csqrt%7B13%7D%7D%7B13%7D)
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
[Right Triangles Only] SOHCAHTOA
[Right Triangles Only] cosθ = adjacent over hypotenuse
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify variables</em>
<em>a</em> = 8
<em>b</em> = 12
<em>c</em>
<u>Step 2: Solve for </u><em><u>c</u></em>
- Substitute in variables [Pythagorean Theorem]: 8² + 12² = c²
- Evaluate exponents: 64 + 144 = c²
- Add: 208 = c²
- [Equality Property] Square root both sides: √208 = c
- Rewrite: c = √208
- Simplify: c = 4√13
<u>Step 3: Define Pt. 2</u>
<em>Identify variables</em>
Angle θ
Adjacent leg = 8
Hypotenuse = 4√13
<u>Step 4: Find</u>
- Substitute in variables [Cosine]:
![\displaystyle cos\theta = \frac{8}{4\sqrt{13}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20cos%5Ctheta%20%3D%20%5Cfrac%7B8%7D%7B4%5Csqrt%7B13%7D%7D)
- Rationalize:
![\displaystyle cos\theta = \frac{2\sqrt{13}}{13}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20cos%5Ctheta%20%3D%20%5Cfrac%7B2%5Csqrt%7B13%7D%7D%7B13%7D)
I think it’s A because all of the numbers seem to be very close together, unlike the other answers.
Answer:
$40
Step-by-step explanation:
200 - 20% = 160
200 - 160 = 40