Task Sets: Apply the Pythagorean Theorem to determine unknown side lengths in right triangles - Common Core Math - Grade 8

Recall / Warm-Up

A right triangle has legs of length $6$ and $8$ . Which side is the hypotenuse, and what is its length?

The hypotenuse is the longest side, opposite the right angle; its length is $10$ .

The hypotenuse is the longest side; its length is $14$ .

The hypotenuse is one of the legs; its length is $8$ .

The hypotenuse is the shortest side; its length is $6$ .

A right triangle has hypotenuse $13$ and one leg of length $5$ . Find the length of the other leg.

While solving a right triangle, a student finds $c^2 = 64$ . What is $c$ ?

$c = 8$

$c = 64$

$c = 32$

$c = 4096$

Fluency Practice

$A right triangle with a horizontal leg labeled 12, a vertical leg labeled 9, a right-angle marker between them, and the hypotenuse labeled with a question mark.$

A right triangle has legs of length $9$ and $12$ . Find the length of the hypotenuse.

A right triangle has legs of length $3$ and $7$ . What is the exact length of the hypotenuse?

$\sqrt{58}$

$10$

$58$

$\sqrt{40}$

$A right triangle with the hypotenuse labeled 17, the horizontal leg labeled 8, a right-angle marker, and the vertical leg labeled with a question mark.$

A right triangle has hypotenuse $17$ and one leg of length $8$ . Find the length of the other leg.

A right triangle has hypotenuse $10$ and one leg of length $4$ . Find the length of the other leg in exact (simplified-radical) form.

A rectangular box is $2$ ft long, $3$ ft wide, and $6$ ft tall. Find the length of its space diagonal (from one bottom corner to the opposite top corner).

Exercises: Finding Unknown Side Lengths with the Pythagorean Theorem (2D and 3D)

Recall / Warm-Up

Fluency Practice