Answer:
The number that belongs in the green box is equal to 909.
General Formulas and Concepts:
Algebra I
Equality Properties
- Multiplication Property of Equality
- Division Property of Equality
- Addition Property of Equality
- Subtraction Property of Equality
Trigonometry
[Right Triangles Only] Pythagorean Theorem:
[tex]\displaystyle a^2 + b^2 = c^2[/tex]
- a is a leg
- b is another leg
- c is the hypotenuse
Step-by-step explanation:
Step 1: Define
Identify given variables.
a = 30
b = 3
c = x
Step 2: Find x
Let's solve for the general equation that allows us to find the hypotenuse:
- [Pythagorean Theorem] Square root both sides [Equality Property]:
[tex]\displaystyle \begin{aligned}a^2 + b^2 = c^2 \rightarrow c = \sqrt{a^2 + b^2}\end{aligned}[/tex]
Now that we have the formula to solve for the hypotenuse, let's figure out what x is equal to:
- [Equation] Substitute in variables:
[tex]\displaystyle \begin{aligned}c & = \sqrt{a^2 + b^2} \\x & = \sqrt{30^2 + 3^2}\end{aligned}[/tex] - Evaluate:
[tex]\displaystyle \begin{aligned}c & = \sqrt{a^2 + b^2} \\x & = \sqrt{30^2 + 3^2} \\& = \boxed{ \sqrt{909} } \\\end{aligned}[/tex]
∴ the hypotenuse length x is equal to √909 and the number under the square root, our answer, is equal to 909.
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Learn more about Trigonometry: https://brainly.com/question/27707750
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Topic: Trigonometry
