Question

For the values a = 8 which is a leg of a right triangle, and value c = 19, which is the hypotenuse, find the length of the other leg, b, to the nearest tenth.
A. 17.7
B. 20.6
C. 17.2
D. 20.3

Answer 1

Hey!

We will have to use the Pythagorean Theorem to solve this. Since we are not looking for the hypotenuse, but rather the length of one of the legs, we will have to use this,
$b^2=c^2-a^2$
Let's plug in the values,
$b^2=19^2-8^2$
Simplify,
$b^2=297$
Since we know that the opposite of a square is the square root, we are going to apply it.
$\sqrt{b^2} = \sqrt{297}$
This tells us that the length of the missing leg would be,
b ≈ 17.2336879396
If we round it to the nearest tenth, our answer would be,
b ≈ 17.2 (answer choice C)

Thanks!
-TetraFish