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Hugo and Brenda are mountain climbing and want to climb up an $8$ -meter vertical rock face. Hugo goes first while Brenda stands a few steps back from the rock face. When Hugo reaches the top, she is $10$ meters away from Brenda. How far away from the rock face is Brenda standing? $\newline$ _____ meters

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Pythagorean Theorem and its converse

Full solution

Q. Hugo and Brenda are mountain climbing and want to climb up an

8

-meter vertical rock face. Hugo goes first while Brenda stands a few steps back from the rock face. When Hugo reaches the top, she is

10

meters away from Brenda. How far away from the rock face is Brenda standing?

\newline

_____ meters

Identify Triangle Formed: Identify the triangle formed by Hugo, Brenda, and the top of the rock face. Brenda's distance from the rock face is one leg, the rock face height ( $8$ meters) is the other leg, and the hypotenuse is the distance from Brenda to Hugo at the top ( $10$ meters).
Set up Pythagorean Theorem: Set up the Pythagorean theorem: $a^2 + b^2 = c^2$ , where $a$ is the rock face ( $8$ meters), $b$ is Brenda's distance from the rock face, and $c$ is the distance from Brenda to Hugo ( $10$ meters).
Plug in Known Values: Plug in the known values: $8^2 + b^2 = 10^2$ . Simplify to find $b^2$ : $64 + b^2 = 100$ .
Solve for b: Solve for $b^2$ : $b^2 = 100 - 64$ , $b^2 = 36$ . Then, find $b$ by taking the square root of $36$ . $b = 6$ .

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