# 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 $$c$$.

• $$c^2=$$

• $$a^2=$$

• $$b^2=$$

(From Unit 8, Lesson 7.)

### 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.

(From Unit 8, Lesson 7.)

### 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.

(From Unit 7, Lesson 15.)

### Problem 5

Evaluate:

1. $$\left(\frac{1}{2}\right)^3$$
2. $$\left(\frac{1}{2}\right)^{\text-3}$$
(From Unit 7, Lesson 6.)

### 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.

1. What does the slope mean in this situation?
2. Based on this model, how heavy would you expect a newborn Doberman to be?
(From Unit 6, Lesson 6.)