Question

An artisan makes pendants in the shape of equilateraltriangles. The height of each pendant is 22mm. What isthe length s of each side of a pendant to the nearesttenth of a millimeter?✓SubmitS22mm

Answer 1

In a 30°-60°-90° triangle the hypotenuse is twice as long as the shorter leg of the triangle, and the longer leg is root 3 as long as the shorter leg.

In this case, S is the hypotenuse and 22mm is the measure of the longer leg.

`\begin{gathered} s=2\cdot\text{shorter leg} \\ s\text{ = hypotenuse} \\ \text{longer leg}=\sqrt[]{3}\cdot\text{shorter leg} \end{gathered}`

We need to find s, but first, we solve for shorter leg as we have the value of the longer leg.

`\begin{gathered} 22=\sqrt[]{3}\cdot\text{shorter leg} \\ \text{shorter leg}=\frac{22}{\sqrt[]{3}} \\ \text{shorter leg}=12.7\text{ mm} \end{gathered}`

Now having the value of the shorter leg, we can calculate S the hypotenuse.

`\begin{gathered} s=2\cdot x \\ s=2\cdot12.7 \\ s=25.4\text{ mm} \end{gathered}`