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Start with an equilateral triangle with all sides of length 2 units and all angles of 60 degrees. Draw the altitude from the apex (top vertex) to the base. Since this is an equilateral triangle, it is easy to show that this line bisects the base.

So now you have a right angled triangle, with a base of 1 and a hypotenuse of 2. Therefore, by Pythagoras, its vertical height is sqrt(3).

Then tan(60) = opposite side/adjacent side = sqrt(3)/1 = 1.7321

It is probably easier if you sketch the diagrams as you go along.

Q: Why the tangent of 60 degrees is 1.7321?

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Tangent of 30 degrees is 0.5770.577

The inverse tangent is 0.83448691252602 degrees.

The tangent of 34 degrees is irrational and so cannot be written in fraction form.

The inverse tangent of 1.4737 (in radians) is .9746 The inverse tangent of 1.4737 (in degrees) is 55.841

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the tangent of 60 degrees is 1.7321

60 * pi / 180

The tangent of 60 degrees is sqrt(3) = 1.732 approx. The shape or size of the triangle is irrelevant.The tangent of 60 degrees is sqrt(3) = 1.732 approx. The shape or size of the triangle is irrelevant.The tangent of 60 degrees is sqrt(3) = 1.732 approx. The shape or size of the triangle is irrelevant.The tangent of 60 degrees is sqrt(3) = 1.732 approx. The shape or size of the triangle is irrelevant.

The tangent of 75 degrees is: 3.7320507852401

Yes, the sine decreases, and so does the tangent.

The tangent of 89 degrees is: 57.3

Tangent of 30 degrees is 0.5770.577

Tangent is 0.5317

The question seems to be incomplete!

Tangent = 0.5

The tangent of 0.47 radians is about 0.508. The tangent of 0.47 degrees is about 0.00820.

The inverse tangent is 0.83448691252602 degrees.