# Find the value of sin60 geometrically

Consider an equilateral ∆ABC with sides AB = BC = CA = 2a.

In triangle ABD, apply Pythagoras theorem to get,

In triangle ABD,

• 160

An equilateral triangle has all angles measuring  60 degrees and all three sides are equal.  For convenience, we choose each side to be length 2.  When you bisect an angle, you get 30 degrees and the side opposite is 1/2 of 2, which gives you 1.  Using that right triangle, you get exact answers for sine of 30°, and sin 60° which are 1/2 and the square root of 3 over 2 respectively.

• 2

An equilateral triangle has all angles measuring  60 degrees and all three sides are equal.  For convenience, we choose each side to be length 2.  When you bisect an angle, you get 30 degrees and the side opposite is 1/2 of 2, which gives you 1.  Using that right triangle, you get exact answers for sine of 30°, and sin 60° which are 1/2 and the square root of 3 over 2 respectively.

• -7

An equilateral triangle has all angles measuring  60 degrees and all three sides are equal.  For convenience, we choose each side to be length 2.  When you bisect an angle, you get 30 degrees and the side opposite is 1/2 of 2, which gives you 1.  Using that right triangle, you get exact answers for sine of 30°, and sin 60° which are 1/2 and the square root of 3 over 2 respectively.

• -1

An equilateral triangle has all angles measuring  60 degrees and all three sides are equal.  For convenience, we choose each side to be length 2.  When you bisect an angle, you get 30 degrees and the side opposite is 1/2 of 2, which gives you 1.  Using that right triangle, you get exact answers for sine of 30°, and sin 60° which are 1/2 and the square root of 3 over 2 respectively.

• -13

An equilateral triangle has all angles measuring  60 degrees and all three sides are equal.  For convenience, we choose each side to be length 2.  When you bisect an angle, you get 30 degrees and the side opposite is 1/2 of 2, which gives you 1.  Using that right triangle, you get exact answers for sine of 30°, and sin 60° which are 1/2 and the square root of 3 over 2 respectively.

• -13

If ABC IS TRI.and hyp.AC=2a,base BC=underroot 3 a and perpendicular AB =a

then  sin 60=BC/AC

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