Trouble with Triangles

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.

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.

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.

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.