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

a = 6.3mm

Explanation:

Use Pythagoras theorem here

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

Rearrange for a by subtracting
`b^(2)` from both sides of the equation

`a^(2) + b^(2) -b^(2) = c^(2) -b^(2)`

Simplify

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

Substitute in our numbers and solve for a

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

`a^(2)` = 68.89 - 29.16

`a^(2)` = 39.73

a =
`√(39.73)`

a = 6.3mm