More Trouble with Triangles

Learning Goal

Students will learn how to apply the Pythagorean Theorem in multi-step, 3-dimensional, and/or real-world situations.

Visual 1: Click and drag the points to fit the triangles to the tent. (Not drawn to scale.)

Question 1: Use the Visual to...

Understand the story.[br][br]An old tent was set up for a camp out. One side of the tent is 6.5 ft with a base of 4.3 ft, and the other side of the tent is 7.1 ft. [br][br]What is the length of the other base?[br][br][b][color=#ff7700]Hint:[/color][/b] What else is unknown, and how can you find it?

Question 1: Check you answer.

Visual 2: Click and drag the pyramid to see it from different angles.

Question 2: Use the Visual to...

Understand this story.[br][br]A 3-D pyramid has a 100 m square base, and a side length of 100 m. [br][br]What is the height of the pyramid?[br][br][b][color=#ff7700]Hint:[/color][/b] Use more than one right triangle.

Question 2: Check your answer.

Visual 3: Positions on a basketball court are shown. Click and drag the basketballs to see them move.

Question 3: Use the Visual to...

Understand this story.[br][br]Two friends are shooting hoops on a non-regulation basketball court. Hunter is 4.12 yds directly sideways from the center when he throws the ball 9.9 yds to the hoop. Casey runs 7.42 yds diagonally from the center, then turns a perfect 90 degrees to shoot.[br][br]How far did Casey throw the ball?[br][br][b][color=#ff7700]Hint:[/color][/b] What else is unknown, and how can you find it?

Question 3: Check your answer.

Visual 4: Click and drag the rectangular prism to see it from different angles.

Question 4: Use the Visual to...

Understand this story.[br][br]A 3-D rectangular prism has a 2 cm by 3 cm base and a 4 cm height.[br][br]What is the diagonal length of the rectangular prism?[br][br][color=#1e84cc][b]Bonus:[/b] [/color]Find two ways to solve the problem.[br][br][b][color=#ff7700]Hint:[/color][/b] Use more than one right triangle.[br]