Prove that Cos60°=1/2????
Answers
Answer:
Draw a Right Angled Triangle with One angle 60 Degrees. Thus this becomes a 30–60–90 Degrees Triangle. Let’s call it a Triangle ABC. Let angle A be 60 Degrees, let angle B be 90 Degrees, so naturally angle C is 30 Degrees.
For a 30–60–90 Degrees Triangle, side opposite to angle 30 Degrees is half the hypotenuse. So in our case if side AB is x then side AC is 2x and side BC is
sqrt(3)*x.
In a Right Angled Triangle, Cos of certain angle is defined as Adjacent Side divided by Hypotenuse.
Therefore Cos(60) would be AB/AC, which is x/2x, which is 1/2.
Thus it is proved that Cos(60) is 1/2.
Other method....
Draw an equilateral triangle ABC.
Let BC be horizontal and A above BC.
All angles 60°
All sides equal length.
Let AD be perpendicular to BC
D is mid point of BC.
cos B = BD / AB
cos 60° = BD / AB
Answer will be 1/2
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Step-by-step explanation:
Draw a Right Angled Triangle with One angle 60 Degrees. Thus this becomes a 30–60–90 Degrees Triangle. Let’s call it a Triangle ABC. Let angle A be 60 Degrees, let angle B be 90 Degrees, so naturally angle C is 30 Degrees.
For a 30–60–90 Degrees Triangle, side opposite to angle 30 Degrees is half the hypotenuse. So in our case if side AB is x then side AC is 2x and side BC is
sqrt(3)*x.
In a Right Angled Triangle, Cos of certain angle is defined as Adjacent Side divided by Hypotenuse.
Therefore Cos(60) would be AB/AC, which is x/2x, which is 1/2.
Thus it is proved that Cos(60) is 1/2.
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