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 √(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.