Finding Unknown Side Lengths

Sidekick Check

Student Summary

The Pythagorean Theorem can be used to find an unknown side length in a right triangle as long as the length of the other two sides is known.

For example, here is a right triangle, where one leg has a length of 5 units, the hypotenuse has a length of 10 units, and the length of the other leg is represented by gg.

A right triangle, where one leg has a length of 5 units, the hypotenuse has a length of 10 units, and the length of the other leg is represented by the letter g.

Start with a2+b2=c2a^2+b^2=c^2, make substitutions, and solve for the unknown value. Remember that cc represents the hypotenuse, the side opposite the right angle. For this triangle, the hypotenuse is 10.

a2+b2=c252+g2=102g2=102−52g2=100−25g2=75g=75\begin{aligned} a^2+b^2&=c^2 \\ 5^2+g^2&=10^2 \\ g^2&=10^2-5^2 \\ g^2&=100-25 \\ g^2&=75 \\ g&=\sqrt{75} \\ \end{aligned}

Use estimation strategies to know that the length of the other leg is between 8 and 9 units, since 75 is between 64 and 81. A calculator with a square root function gives 75 ≈8.66\sqrt{75} \approx 8.66.

Visual / Anchor Chart

Standards

Addressing
8.G.7

Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real world and mathematical problems in two and three dimensions.

Building Toward
8.G.B

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