Sin is opposite over hypotenuse.
Just think of this to help you:
SOH-CAH-TOA
Sine = opposite over hypotenuse
Cosine = adjacent over hypotenuse
Tangent = opposite over adjacent
Hope that helps you.
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The solution relies on using the sine rule.Suppose that the perimeter of triangle ABC is P.Then you need to divide P into 3 parts in the ratio of sin(A) : sin(B) : sin(C).Let sin(A) + sin(B) + sin(C) = X. ThenAB = P*sin(C)/XBC = P*sin(A)/XCA = P*sin(B)/X
The longest side of the triangle will always be opposite the largest angle, which is 90° in this case. We can use the sine law to work out the other sides with that: sin(90°) / 18 = sin(60°) / x = sin(30°) / y 1/18 = sin(60°) / x x = 18 sin(60°) x = 18√3 / 2 x = 9√3 1/18 = sin(30°) / y y = 18 sin(30°) y = 9 So the triangle has a sides of 9 and 9√3, with a hypotenuse of 18
sin θ = cos (90° - θ) cos θ = sin (90° - θ)
An equilateral triangle has 3 equal interior angles each of 60 degrees. There are two right angled triangles in an equilateral triangle. So we can use trigonometry to find the length of one side of the equilateral triangle then multiply this by 3 to find its perimeter. Hypotenuse (which is one side of the equilateral) = 15/sin 60 degrees = 17.32050808 17.32050808 x 3 = 51.96152423 Perimeter = 51.96152423 units.
sin of angle a = opposite/hypotenuse = 1/3 sin-1(1/3) = 19.47122063 degrees