Question

Find the required unknown angle of the following triangles using a calculator

Answer 1

To find the required side, we will make use of the Pythagorean theorem which says: The square of the longest side (the hypotenuse) is equal to the sum of the squares of the other two sides.

Hence from Pythagoras theorem, that means

`9^2=3^2+x^2`

That is, let's take the unknown side as x, using the euqation to find x, we have

`\begin{gathered} 9^2=3^2+x^2 \\ 81=9+x^2 \\ \text{collecting like terms } \\ 81-9=x^2 \\ 72=x^2 \\ x^2=72 \\ \text{taking the square to the other side, it becomes square root } \\ x=\sqrt[]{72} \\ x=8.48528 \\ x=8.49\text{ to the nearest hundredth } \end{gathered}`

Hence the answer is 8.49 to the nearest hundredth