Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Sketch each situation, mark the right angle, and decide which side is the hypotenuse before writing the equation.
Standards: 8.G.B.6, 8.G.B.7 · Level: Grade 8
Problem 1 Find the hypotenuse ★★★
Calculate the hypotenuse of a right triangle whose legs are 20 and 21 units long.
Problem 2 Find a leg ★★★
One leg of a right triangle is 8 units and the hypotenuse is 17 units. Calculate the second leg.
Problem 3 Irrational hypotenuse ★★★
Calculate the hypotenuse, rounded to the nearest tenth, when the two legs measure 6 and 7 units.
Problem 4 Leg to the nearest tenth ★★★
Round to the nearest tenth: how long is the second leg when the hypotenuse is 13 and one leg is 9?
Problem 5 Is it a right triangle? ★★★
Use the converse to decide whether side lengths 9, 40, and 41 describe a right triangle.
Problem 6 Read the figure ★★★
Use the figure to calculate the hypotenuse.
Problem 7 Not a right triangle ★★★
Explain whether side lengths 10, 11, and 15 can form a right triangle.
Problem 8 Find x ★★★
Find x in the figure.
Problem 9 Areas of squares ★★★
The squares built on the two legs of a right triangle have areas 25 and 144. Find the length of the hypotenuse.
Problem 10 Short ladder ★★★
A 10-foot ladder stands with its base 3.5 feet from a wall. How high up the wall does it reach? Round to the nearest tenth.
Problem 11 TV size ★★★
A TV screen is 48 inches wide and 27 inches tall. Find the diagonal length to the nearest inch.
Problem 12 Right or not? ★★★
Is a triangle with sides 1.5, 2, and 2.5 meters a right triangle?
Problem 13 Across the field ★★★
A rectangular field is 45 yards by 108 yards. How long is its diagonal?
Problem 14 Isosceles right triangle ★★★
Each leg of an isosceles right triangle is 12 centimeters. Find the hypotenuse, exactly and to the nearest tenth.
Problem 15 Fire truck ladder ★★★
A fire truck ladder is 26 feet long. Its base is 10 feet from a building. How high on the building does it reach?
Problem 16 Baseball throw ★★★
A youth baseball diamond is a square with sides of 60 feet. A catcher throws from home plate to second base. How far is the throw, to the nearest tenth of a foot?
Problem 17 Wheelchair ramp ★★★
A ramp rises 2.5 feet over a horizontal run of 30 feet. How long is the sloping surface of the ramp, to the nearest tenth of a foot?
Problem 18 Shipping box ★★★
A shipping box measures 12 inches by 16 inches by 21 inches. What is the length of the longest straight rod that fits inside?
Problem 19 Drone flight ★★★
A drone flies 36 meters east, then 15 meters north, then climbs straight up 20 meters. Find its distance from the starting point, to the nearest tenth of a meter.
Problem 20 Is the deck square? ★★★
A carpenter marks a corner of a deck with sides 2.4 meters and 3.2 meters. The diagonal measures 4.1 meters. Is the corner a right angle? What should the diagonal be?
