Question

The hypotenuse of a right triangle measures 13 cm and one of its legs measures 12 cm. Find the measure of the other leg. If necessary, round to the nearest tenth.

Answer 1

5 cm

Explanation:

Given two sides of a right triangle, we can find the other side using the Pythagorean theorem, which is

`a^2+b^2=c^2`, where a and b are any of the two legs (e.g., you can set 12 can be a or b) and c is the hypotenuse.

If we allow 12 to b a and 13 to be c, we can solve for b, which is the measure of the other side:

`12^2+b^2=13^2\\144+b^2=169\\b^2=25\\b=5\\b=-5`

When taking the square root of a number, you always get a negative number and a positive number, since squaring a negative gives a positive answer (e.g. 5^2 = 25 and (-5)^2 = 25). However, because you can't have a negative answer, the answer is simply b = 5 cm

We can even check our answer by making sure that the sum of the square of the two legs equals the square of the hypotenuse:

`12^2+5^2=13^2\\144+25=169\\169=169`