Question

Use the Pythagorean Theorem to find the length of the hypotenuse in the righttriangle shown below. (Round your answer to the nearest tenth.)

Answer 1

Let us remember the Pythagoras theorem by a diagram

That is, in a rectangle triangle the square of the measure of the longer side (the hypotenuse) is equal to the sum of the squares of the measures of the other two sides.

To solve the question, we have to identify the longer side (the hypotenuse) and apply the theorem.

Looking at the picture, we identify that:

Therefore the side that we have to find is the side a, in the diagram above. From the Pythagoras Theorem, we must have :

`\begin{gathered} a^2=b^2+c^2 \\ a^2=9^2+9^2 \\ a^2=81+81 \\ a^2=162 \end{gathered}`

Therefore, to finish we take the square root on both sides and consider only the positive square root, because we are finding a length.

`a=√(162)\approx\text{ 12.7}`

We conclude that the hypotenuse measures 12.7 , where we have approximated to the nearest tenth as required in the question.