Question

In a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse. If a=24 meters and c=51 meters, what is b? If necessary, round to the nearest tenth.

Answer 1

Answer: b = 45

Explanation:

According to the Pythagorean Theorem of a right triangle, the square of leg a plus the square of leg b equals the square of c (the hypotenuse). This can be mathematically expressed as
`a^(2) + b^(2) = c^(2)`.

Using the formula, we solve as follows:

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

(Insert the given numbers)

`24^(2) + b^(2) = 51^(2)`

(Simplify the exponents)

`576 + b^(2) = 2,601`

(Subtract 576 from both sides)

`b^(2) = 2,025`

(Simplify by finding the square root of each number)

`\sqrt{b^(2) } = √(2,025)`

Answer

`b = 45`