What is the exact value of tan 30?

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Answer 1 · 2018-06-04T08:37:57

See explanation below

In a equilateral triangle, all sides are equal to 1. Then all angles are 60º

Consider the height of this triangle. So we have an right triangle with sides 1/2, 1 and h=height. The angles are 90, 60 and 30

Lets calculate the height by Pitogorean theorem

${(\frac{1}{2})}^{2} + h^{2} = 1^{1}$ $(1/2)^2+h^2=1^1$ , then $h = \frac{\sqrt{3}}{2}$ $h=sqrt3/2$

Then $sin 30 = \frac{\frac{1}{2}}{1} = \frac{1}{2}$ $sin30=(1/2)/1=1/2$

$cos 30 = \frac{\sqrt{3}}{2}$ $cos30=sqrt3/2$

$tan 30 = \frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}} = \frac{1}{\sqrt{3}} = \frac{\sqrt{3}}{3}$ $tan30=(1/2)/(sqrt3/2)=1/(sqrt3)=sqrt3/3$