# Lesson Worksheet: Applications on the Pythagorean Theorem Mathematics • 8th Grade

In this worksheet, we will practice applying the Pythagorean theorem in geometric questions and real-life situations.

**Q5: **

Determine, to the nearest tenth of an inch, the length of the diagonal of a door of length 88 inches and width 34 inches.

**Q7: **

Emma and Scarlett are communicating by walkie-talkie with a range of 42 feet. Reaching a 22 ft long bridge, Emma waits while Scarlett crosses and then walks up the bank until she can no longer hear Emma. How far up the river did she walk? Give your answer to one decimal place.

**Q8: **

A tree, which was growing perpendicular to the ground, was 3 m tall. It snapped at a point that was 1 m above the ground. The top part of the tree fell and hit the ground. However, at the point of the break, the tree remained connected. Find the distance between the base of the tree and the point where the top of the tree touches the ground.

- A1 m
- B m
- C m
- D m
- E m

**Q10: **

A space station is orbiting Earth at an altitude of 498 miles above the surface. Assuming the radius of the Earth is 4,000 miles, determine, to the nearest mile, the distance between the space station and the farthest point on the Earth’s surface from which it could be seen.