Multiple choice

A right triangle has one leg that measures 172.8 inches and a hypotenuse that measures 787.2 inches. What is the length, in inches, of the other leg of the triangle?

  1. 488

  2. 678

  3. 768

  4. 786
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Using the Pythagorean theorem: a^2 + b^2 = c^2. 172.8^2 + b^2 = 787.2^2. b^2 = 787.2^2 - 172.8^2 = (787.2 - 172.8)(787.2 + 172.8) = 614.4 * 960 = 589824. b = sqrt(589824) = 768.

AI explanation

By the Pythagorean theorem, the square of the hypotenuse equals the sum of the squares of the two legs, giving the equation 787.2 squared equals 172.8 squared plus the other leg squared. Converting the decimals to fractions reveals the hypotenuse is 3936/5 and the known leg is 864/5, meaning the unknown length is the square root of ((3936/5) squared minus (864/5) squared). Factoring out 1/5 and recognizing the difference of squares gives 1/5 times the square root of (4800 times 3072), which simplifies exactly to 768.

Keep practicing — related questions