Answer with explanation I will and rate on the feedback. Will mark brainliest too

Mathematics

1 answer:

yarga [219]3 years ago

6 0

Answer: 6.6

Step-by-step explanation:

We have two triangles. Find the hypothenuse of the first triangle to make it easier to solve the second triangle.

First triangle:

a = 6

b = 8

c = ?

Use pythagorean's theorem

$c^2=a^2+b^2\\c=\sqrt{a^2+b^2}$

$c=\sqrt{(6)^2+(8)^2}\\ c=\sqrt{36+64}\\ c=\sqrt{100}\\ c=10$

This hypothenuse is valid for both triangles. Having said this, we already have 2 sides of the second triangle; c and a. We need to find b.

$c^2=a^2+b^2\\b^2=c^2-a^2\\b=\sqrt{c^2-a^2}$

$b=\sqrt{(12)^2-(10)^2}\\ b=\sqrt{144-100}\\ b=\sqrt{44}\\ b=6.6$

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3 years ago

Please help! acellus

ch4aika [34]

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:
$\displaystyle a^2 + b^2 = c^2$

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]:
$\displaystyle \begin{aligned}a^2 + b^2 = c^2 \rightarrow c = \sqrt{a^2 + b^2}\end{aligned}$

Now that we have the formula to solve for the hypotenuse, let's figure out what x is equal to:

[Equation] Substitute in variables:
$\displaystyle \begin{aligned}c & = \sqrt{a^2 + b^2} \\x & = \sqrt{30^2 + 3^2}\end{aligned}$
Evaluate:
$\displaystyle \begin{aligned}c & = \sqrt{a^2 + b^2} \\x & = \sqrt{30^2 + 3^2} \\& = \boxed{ \sqrt{909} } \\\end{aligned}$