Question

Approximate the length of the hypotenuse to the nearest tenth using a calculator. The hypotenuse is about units long.

Answer 1

Notice that although the image provided doesn't contain written values for the "leg"of the right angle triangle, you can count the number of squares/divisions that each leg hes. one of them is 6 units long, and the other one is 7 units (or divisions) long.

So we can use 6 and 7 as the sizes for the two legs of the right angle triangle.

Now using Pythagoras' Theorem, we can estimate the length of the hypotenise in the same units as the other sides:

`\begin{gathered} \text{hypotenuse=}\sqrt[]{6^2+7^2_{}} \\ \text{hypotenuse}=\sqrt[]{36+49} \\ \text{hypotenuse}=\sqrt[]{85} \end{gathered}`

This is the EXACT value of the hypotenuse. but we are asked to find its approximate value in decimal form. So we use a calculator for that, obtaining:

hypotenuse = 9.2195 which rounded to the nearest tenth gives:

hypotenuse = 9.2 units long