Question

The variables a and b represent the legs of a right triangle. The variable c represents the hypotenuse. Use the Pythagorean theorem to find the missing side. Write exact answers using radicals when necessary. A = 3, c = 5, find b.

Answer 1

Given:

a and b are two legs of a right triangle and c is hypotenuse.

a=3 and c=5

To find:

The value of b.

Solution:

According to the Pythagoras theorem,

$hypotenuse^2=(leg_1)^2+(leg_2)^2$

Using Pythagoras theorem, we get

$c^2=(a)^2+(b)^2$

Now, putting a=3 and c=5, we get

$5^2=(3)^2+b^2$

$25=9+b^2$

$25-9=b^2$

$16=b^2$

Taking square root on both sides.

$\pm \sqrt{16}=b$

$\pm 4=b$

The measure of side of a triangle cannot be negative. So, only value of b is 4.

Therefore, the value of b is 4.