Lesson 8
Finding Unknown Side Lengths
Let’s find missing side lengths of right triangles.
Problem 1
Find the exact value of each variable that represents a side length in a right triangle.
Problem 2
A right triangle has side lengths of \(a\), \(b\), and \(c\) units. The longest side has a length of \(c\) units. Complete each equation to show three relations among \(a\), \(b\), and \(c\).

\(c^2=\)

\(a^2=\)

\(b^2=\)
Problem 3
What is the exact length of each line segment? Explain or show your reasoning. (Each grid square represents 1 square unit.)
a.
b.
c.
Problem 4
In 2015, there were roughly \(1 \times 10^6\) high school football players and \(2 \times 10^3\) professional football players in the United States. About how many times more high school football players are there? Explain how you know.
Problem 5
Evaluate:
 \(\left(\frac{1}{2}\right)^3\)
 \(\left(\frac{1}{2}\right)^{\text3}\)
Problem 6
Here is a scatter plot of weight vs. age for different Dobermans. The model, represented by \(y = 2.45x + 1.22\), is graphed with the scatter plot. Here, \(x\) represents age in weeks, and \(y\) represents weight in pounds.
 What does the slope mean in this situation?
 Based on this model, how heavy would you expect a newborn Doberman to be?