Height 2

Calculate the height of the equilateral triangle with side 27.

Correct result:

h =  23.4

Solution:

$$\begin{gathered} a=27 \\ {h}^2+(a\mathrm{/}2{)}^2=a^2 \\ {h}^2=a^2-a^2\mathrm{/}4 \\ {h}^2=3\mathrm{/}4\cdot a^2 \\ h=a\cdot {\displaystyle \frac{\sqrt{3}}{2}}=27\cdot {\displaystyle \frac{\sqrt{3}}{2}}\doteq 23.3827 \\ \text{ Verifying Solution: } \\ h=a\cdot \sin 60^{\circ }=\sin \pi \mathrm{/}3=23.4 \end{gathered}$$

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