Lesson 8

Finding Unknown Side Lengths

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Problem 1

Find the exact value of each variable that represents a side length in a right triangle.

5 right triangles. 

 

Solution

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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 \(c\).

  • \(c^2=\)

  • \(a^2=\)

  • \(b^2=\)

 

Solution

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(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.

A line segment labeled l on a square grid. One endpoint is 4 units directly down from the other endpoint.
A line segment slanted upward and to the right, labeled m, on a square grid. The top endpoint is 2 units up and 4 units to the right from the bottom endpoint.
A line segment labeled “q” on a square grid. 

Solution

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(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.

 

Solution

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(From Unit 7, Lesson 15.)

Problem 5

Evaluate:

  1. \(\left(\frac{1}{2}\right)^3\)
  2. \(\left(\frac{1}{2}\right)^{\text-3}\)

Solution

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(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.

Scatter plot with line of best fit. Horizontal axis, age in weeks, scale 0 to 25, by 5’s. Vertical axis, weight in pounds, scale 0 to 80, by 20’s. 
  1. What does the slope mean in this situation?
  2. Based on this model, how heavy would you expect a newborn Doberman to be?

Solution

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(From Unit 6, Lesson 6.)