The image is a graphical representation of a right triangle with a right angle at the bottom left. The sides of the triangle are labeled with the letters $X$X, $Y$Y, and $Z$Z. The hypotenuse is labeled $X$X, the vertical leg is labeled $Z$Z, and the base or horizontal leg is labeled $Y$Y. At the bottom left corner, where the vertical and horizontal legs meet at a right angle, there is a square outline which is colored in a light blue to indicate the right angle.

$X$X

$Y$Y

$Z$Z

Easy

< 1min

If $3$3 and $4$4 are the two smallest values in a Pythagorean triple, what is the largest value, $c$c, in the triple?

Easy

1min

Using your knowledge of common Pythagorean triples , find the hypotenuse in a triangle with shorter side lengths $15$15 units and $36$36 units.

Easy

1min

If $x$x, $y$y, and $z$z are three sides of a right triangle, will side lengths of $4x$4x, $4y$4y and $4z$4z make a right triangle as well?

Easy

< 1min

Outcomes

G.N.Q.A.1

Use units as a way to understand real-world problems.*

G.N.Q.A.1.A

Use appropriate quantities in formulas, converting units as necessary.

G.SRT.C.5

Solve triangles.*

G.SRT.C.5.A

Know and use the Pythagorean Theorem and trigonometric ratios (sine, cosine, tangent, and their inverses) to solve right triangles in a real-world context.

G.MP1

Make sense of problems and persevere in solving them.

G.MP2

Reason abstractly and quantitatively.

G.MP3

Construct viable arguments and critique the reasoning of others.

G.MP4

Model with mathematics.

G.MP5

Use appropriate tools strategically.

G.MP6

Attend to precision.

G.MP7

Look for and make use of structure.

G.MP8

Look for and express regularity in repeated reasoning.

8.01 Right triangles and the Pythagorean theorem

Interactive practice questions

Outcomes

G.N.Q.A.1

G.N.Q.A.1.A

G.SRT.C.5

G.SRT.C.5.A

G.MP1

G.MP2

G.MP3

G.MP4

G.MP5

G.MP6

G.MP7

G.MP8

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