Question

For the right triangle shown, the lengths of two sides are given. find the third side. leave your answer in simplified, radical form.b = 9, c = 16

Answer 1

Answer:

5√7

Step-by-step explanation:

c is the hypotenuse NOT the leg (I just took a quiz and had the exact same question). Therefore:

16^2 - 9^2  = a^2

256 - 81 = a^2

175 = a^2

a^2 = 5√7

Answer 2

If c is the hypotenuse and b is the leg, then the third side (a):
$a= \sqrt{c^2-b^2}= \sqrt{16^2-9^2}= \sqrt{256-81}= \sqrt{175}=5 \sqrt{7}$

If b and с are legs, then hypotenuse (a):
$a= \sqrt{b^2+c^2}= \sqrt{9^2+16^2}= \sqrt{81+256}= \sqrt{337}$