Trouble with Triangles

Author:: Tamara Willis

Topic:: Pythagoras or Pythagorean Theorem, Triangles

Learning Goal

Students will learn how to apply the Pythagorean Theorem in simple, 2-dimensional, real-world situations.

Visual 1: Click and drag the points to see the ladder move.

Question 1: Use the Visual to...

Understand the story. Some work needs to be done on the side of an old building about 10 ft up. A ladder will be used, but it needs to be grounded 5 ft away from the side of the building to be safe. What is the missing piece in this story? Find the value of the missing piece.

Question 1: Check you answer.

Visual 2: Click and drag the points to fit the triangle to the ramp. (Not drawn to scale.)

Question 2: Use the Visual to...

Understand this story. A carpenter is building a wooden ramp for the local skate park. To make the ramp as safe as possible, he researched that the ramp itself should be 3 yds long, the supporting length should be 2.5 yds, and the supporting height should be 0.5 yds. He might have mixed up his math somewhere, so he wants to double check that this ramp will be a perfectly stable right triangle before building. What is the missing piece in this story? Find the value of the missing piece.

Question 2: Check your answer.

Visual 3: Click and drag the point to see the hot air balloon move.

Question 3: Use the Visual to...

Understand this story. A hot air balloon guide takes a balloon straight up into the air, then throws a 50 m rope down to the ground where it’s tied down. The wind starts to pick up and blows the balloon 40 m away from where it started. What is the missing piece in this story? Find the value of the missing piece.

Question 3: Check your answer.

Visual 4: Click and drag the points to fit the triangle to the points on the map. (Not drawn to scale.)

Question 4: Use the Visual to...

Understand this story. Two curious math students are playing around with Moogle Gaps^TM. They see that their houses are about 2.663 mi apart, and they notice their favorite hangout, the neighborhood taqueria, is about 1.5 mi from one of their houses and 2.2 mi from their other house. The route really looks like a right triangle. What is the missing piece in this story? Find the value of the missing piece.