Question

) In a right triangle, a and b are the lengths of the legs and c is the length of the

hypotenuse. If b = 5.4 millimeters and c= 8.3 millimeters, what is a? If necessary, round to

the nearest tenth.

Answer 1

If b is equal to 5.4 millimeters and c is equal to 8.3 millimeters, then a has to be equal to 6.3 millimeters.

Explanation:

1. Know the Pythagorean Theorem

`a^2+b^2=c^2`

2. Rearrange the equation so we can find a.

`a^2=c^2-b^2`

3. Plug in the numbers for b and c because that is what we are given in the problem.

`a^2=8.3^2-5.4^2`

4. Simplify the expressions.

`a^2=68.89-29.16`

5. Subtract 29.16 from 68.89.

`a^2=39.73`

6. Square root the expressions on both sides of the equation.

`√(a^2)=√(39.73)`

7. Simplify the equation.

`a=6.3`

Answer 2

6.3 mm

Explanation:

The Pythagorean theorem tells you ...

c^2 = a^2 + b^2

Solving for "a", you get

a = √(c^2 -b^2)

a = √(8.3^2 -5.4^2) = √39.73

a ≈ 6.3 . . . . mm

The length of "a" is about 6.3 mm.