ABC is a triangle in which the angle B = 60 degree and the angle C = 30 degree. Prove that BC = 2AB.
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
Cross multiply to get final answer:
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.
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
But sine 30=1/2
Using the cross multiplying