Lesson 8: Practice Problems

Problem 1

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

  1. A right triangle with legs 8 and h and hypotenuse 10.
  2. A right triangle with legs 6 and k and hypotenuse 6.5.
  3. A right triangle with legs 2 and m and hypotenuse 5.
  4. A right triangle with legs square root of 10 and n and hypotenuse 10.
  5. A right triangle with legs square root of 68 and p and hypotenuse square root of 85.

Problem 2 From Unit 8 Lesson 7

A right triangle has side lengths of , , and units. The longest side has a length of units. Complete each equation to show three relations among , , and .

Problem 3 From Unit 8 Lesson 7

What is the exact length of each line segment? Explain or show your reasoning. (Each grid square represents 1 square unit.)

  1. A line segment labeled l on a square grid. One endpoint is 4 units directly down from the other endpoint.
  2. 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.
  3. A line segment labeled “q” on a square grid. The line segment starts at an intersection point on the grid and slants upward and to the right to an end point that is 4 units to the right and 5 units up.

Problem 4 From Unit 7 Lesson 15

In 2015, there were roughly high school football players and professional football players in the United States. About how many times more high school football players are there? Explain how you know.

Problem 5 From Unit 7 Lesson 6

Evaluate:

Problem 6 From Unit 6 Lesson 6

Here is a scatter plot of weight vs. age for different Dobermans. The model, represented by , is graphed with the scatter plot. Here, represents age in weeks, and represents weight in pounds.

A scatter plot of age (weeks) (horizontal from 0-25) and weight (pounds) (vertical from 0 to 80), with a line of best fit sloping upwards.

  1. What does the slope mean in this situation?

  2. Based on this model, how heavy would you expect a newborn Doberman to be?