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.

Q1:

A window cleaner has a ladder that is 8.1 meters long. If he places it on the ground such that its top is at a window that is 6.76 meters above the ground, determine the distance between the base of the ladder and the wall, and round the result to the nearest hundredth.

Q2:

Benjamin traveled north for 19 miles and then east for 13 miles. Determine, to the nearest tenth of a mile, how far he is from his starting point.

Q3:

A ladder of height 24 feet leaning against a wall reaches a window 19 feet above the ground. To the nearest tenth, how far from the building is the bottom of the ladder?

Q4:

A dining table is 24 ft long and 12 ft wide. Determine, to the nearest tenth, how far it is from one corner to the diagonally opposite corner.

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.

Q6:

Liam has a rectangular back yard. He measured one side of the yard and found it to be 85 feet and its diagonal to be 117 feet. Determine, to the nearest tenth of a foot, the length of the other side of his back yard.

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
  • B5 m
  • C5 m
  • D3 m
  • E3 m

Q9:

The figure shows a 129 m long bridge on supports 𝑀𝐶, 𝑀𝐷 attached at the midpoint 𝑀. If 𝐴𝐶=51.6m, find the length of 𝑀𝐶 to the nearest hundredth.

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.

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