Question

one leg of a right triangle is 10 units, and its hypotenuse is 12 units. what is the length of the other leg?
a. about 7 units
b. about 15 units
c. about 25 units
d. about 122 units
e. about 224 units

Explanation:

Step1: Apply Pythagorean theorem

Let the known leg be $a = 10$, the hypotenuse be $c=12$, and the unknown leg be $b$. The Pythagorean theorem is $a^{2}+b^{2}=c^{2}$, so $b^{2}=c^{2}-a^{2}$.

Step2: Substitute values

Substitute $a = 10$ and $c = 12$ into the formula: $b^{2}=12^{2}-10^{2}=144 - 100=44$.

Step3: Solve for $b$

Take the square - root of both sides: $b=\sqrt{44}\approx 6.63\approx7$.

Answer:

A. about 7 units