Finding Unknown Side Lengths

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

8.G.B.7

Building Toward
8.G.B

8.G.B

8.G.B

8.G.B