EQL triangle

Calculate the inradius and circumradius of an equilateral triangle with side a=77 cm.

Correct answer:

r₁ =  22.2 cm
r₂ =  44.5 cm

Step-by-step explanation:

$$\begin{gathered} \tan 30^{\circ }={\displaystyle \frac{r_1}{{\displaystyle \frac{77}{2}}}} \\ {r}_1={\displaystyle \frac{77}{2}}\tan 30^{\circ }=22.2\text{ cm} \end{gathered}$$

$$\begin{gathered} \cos 30^{\circ }={\displaystyle \frac{{\displaystyle \frac{77}{2}}}{r_2}} \\ {r}_2={\displaystyle \frac{77}{2}}\mathrm{/}\cos 30^{\circ }=44.5\text{ cm} \end{gathered}$$

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