# ABC is a triangle in which the angle B = 60 degree and the angle C = 30 degree. Prove that BC = 2AB.

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ABC is a triangle. Angle B is 60 degrees while Angle C is 30 degrees. Since the sum of angles in a triangle adds up to 180 degrees, angle A would be= 180-90= 90 degrees (that means triangle ABC is a right-angle triangle)

Since you want to prove BC=2AB

We would use the side AB and BC so as to use trigonometrical ratios for this relationship.

Thus, cos 60 degree= AB/BC (cosine= adjacent/hypotenuse and AB is adjacent side, BC is the hypotenuse)

Since cos 60 degree equals to a value of 1/2

1/2= AB/BC

Cross multiply to get final answer:

**BC=2AB **(proven)

If ABC is a triangle where the angle B=60 degree and the angle C=30 degree, then, knowing the fact that the sum of all 3 angles in a triangle is 180 degree, that means that the angle A= 90 degree.

A+B+C=180

A+60+30=180

A=180-60-30

A=90

So, the ABC triangle is a right triangle, where A angle has 90 degree.

In this triangle, we can use the definition of sine trigonometric function, for the angle B=30.

The definition for the sine trigonometric function says that the sine of an angle is the ratio between the opposite cathetus and hypotenuse.

The opposite cathetus of B angle is AB and the hypotenuse is BC.

sine B= AB/BC

sine 30=AB/BC

But sine 30=1/2

1/2=AB/BC

Using the cross multiplying

BC=2AB