Question

The hypotenuse of a triangle is 12 feet long. One leg is8 feet long. What is the length of the other leg? Expressyour answer in simplest radical form. Don't forget towrite your reasons.

Answer 1

Answer:

The other leg = 4√5

Explanations:

The Pythagora's theorem states that the square of the hypotenuse equals the sum of the squares of the other two sides

`\text{Hypotenuse}^2=Opposite^2+Adjacent^2`

Hypotenuse, c = 12

Opposite, a = 8

Adjacent, b = ?

`\begin{gathered} c^2=a^2+b^2\text{ } \\ 12^2=8^2+b^2 \\ 144=64+b^2 \\ 144-64=b^2 \\ 80=b^2 \\ b^2\text{ = 80} \\ b\text{ = }\sqrt[]{80} \\ b\text{ = }4\sqrt[]{5} \end{gathered}`

The other leg is 4√5