Question

a sheet metal worker needs to cut a piece of metal in the shape shown below what is the length of the longest side of the triangle

Answer 1

The picture shown is a right angled triangle, and the longest side is the hypotenuse, that is, that which is facing the right angle.

The triangle already has a reference angle given, and that is angle 30 degrees, and the side between the right angle and the reference angle is the adjacent. Hence we have the adjacent and the hypotenuse, and we can now use the trig ratio;

`\begin{gathered} \cos 30=\frac{\text{adj}}{\text{hyp}} \\ \cos 30=\frac{18}{\text{hyp}} \\ \cos 30=\frac{\sqrt[]{3}}{2} \\ \frac{\sqrt[]{3}}{2}=(18)/(hyp) \\ \text{Cross multiply and you have;} \\ \text{hyp}=\frac{2*18}{\sqrt[]{3}} \\ Rationalize\text{ and you'll have} \\ \text{hyp}=\frac{36}{\sqrt[]{3}}*\frac{\sqrt[]{3}}{\sqrt[]{3}} \\ \text{hyp}=\frac{36\sqrt[]{3}}{3} \\ \text{hyp}=12\sqrt[]{3} \end{gathered}`

The hypotenuse therefore is 12 squarev