Chapter 13: Triangles 175You can use the Pythagorean theorem to find a leg, too, if you know one leg and the hypotenuse.
Suppose you’re shopping for a new TV, and you’re looking at one that is advertised as 55 inch.
That’s the diagonal measurement, corner to corner, so it’s the hypotenuse of a right triangle. If
that television is 27 inches high, how wide will it be? The height is one leg, and the width you’re
looking for is the other leg, so a = 27, b is unknown, and c = 55.
The TV will be about 48 inches, or 4 feet, wide.
You’ve probably notices a lot of “approximately equal to” answers from the Pythagorean theorem.
That’s because a lot of those square roots produce irrational numbers, whose decimals go on
forever and have to be rounded.
There are some problems that work out to nice whole number answers, and when you work with
right triangles, you get to know them. A set of three whole numbers that fits the Pythagorean
theorem is called a Pythagorean triple. The most common one is 3-4-5: 3^2 + 4^2 = 5^2. Multiples of
Pythagorean triples are also triples, so 6-8-10 and 30-40-50 work as well. Other Pythagorean
triples are 5-12-13 and 8-15-17. These sets of numbers come up a lot in right triangle problems,
and recognizing the triples can save you some work.
DEFINITION
A Pythagorean triple is a set of three whole numbers a, b, and c that fit the rule
a^2 + b^2 = c^2.ab
≈c
b
b
b
b22 2
22 2
2
227 55
729 3,025
3,025 729 2,296
2,296 47.9CHECK POINT
Find the missing side of each right triangle.- In 'XYZ, XY YZ. If XY = 15 cm and YZ = 20 cm, find XZ.
- In 'RST, ST RT. If ST = 20 inches and RS = 52 inches, find RT.
- In 'PQR, PQ PR. If PQ = PR = 3 feet, find QR.
- In 'CAT, CA AT. If CT = 8 meters and CA = 4 meters, find AT.
- In 'DOG, DO OG. If DO = 21 cm and DG = 35 cm, find OG.