Prove cos30= root3/2
Answers
Answered by
9
Consider a right traingle ABC right angles at B such that ∠A=60° and ∠C=30°
Note that if a right triangle has angles 30°, 60° and 90°, then the side opposite to ∠C is exactly one half the hypotenuse.So if the hypotenuse is 2, then the opposite side to ∠C is 1Use pythagoras theorem to get, AB2+BC2=AC2 (1)2+BC2=(2)2 1+BC2=4 BC2=3 BC=3√Now since cosine is the ratio of the length of the base to the length of the hypotenuse.Thuis gives, cosC=BCACwhich further implies that, cos30°=3√2
Note that if a right triangle has angles 30°, 60° and 90°, then the side opposite to ∠C is exactly one half the hypotenuse.So if the hypotenuse is 2, then the opposite side to ∠C is 1Use pythagoras theorem to get, AB2+BC2=AC2 (1)2+BC2=(2)2 1+BC2=4 BC2=3 BC=3√Now since cosine is the ratio of the length of the base to the length of the hypotenuse.Thuis gives, cosC=BCACwhich further implies that, cos30°=3√2
Attachments:
Answered by
2
here is your answer in above picture.....
Attachments:
Similar questions