why does tan 60 degrees equal the square root of 3? If I use a calculator to calculate I get 1.7 but how would I guess square root of 3?

Question

anonymous · Answer

$$\tan 60=\frac{\sin 60}{\cos 60}=\frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}$$

You sure your calculator's using degrees instead of radians?

anonymous · Answer

Okay, according to WolframAlpha: http://www.wolframalpha.com/input/?i=tan+%2860%29 $$\sqrt{3} \approx 1.732...$$

anonymous · Answer

oh there is a whole formula? The book just introduced them... m = tan = dy/dx...

ok must look into tan/cos/sin then..

anonymous · Answer

got the answer but the back says square root of 3 instead of 1.7 so okay thanks it is not a simple answer...

asnaseer · Answer

you can derive the answer by looking at an equilateral triangle:
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in this triangle, the height 'h' of the triangle is found using Pythagorus as:$$h=\sqrt{x^2-\frac{x^2}{4}}=\sqrt{\frac{3x^2}{4}}=\frac{x\sqrt{3}}{2}$$so we can see then that:$$\tan(60)=\frac{h}{\frac{x}{2}}=\frac{\frac{x\sqrt{3}}{2}}{\frac{x}{2}}=\sqrt{3}$$