Math 9 - Sine Law

The Law of Sine
The Law of Sines does tell us that for any triangle, the ratio of any side length to the sine of the angle opposite that side is equal to the ratio of any other side length to the sine of the angle opposite that other side.
Using Right Triangle Trigonometry, prove the Law of Sines[code][/code]. [br]Refer to Triangle ABC above. The first one is done for you. [br][br]Tick the first box. [br]We can use the sine function to find an expression for [b]h[/b] in the [color=#ff0000][b]red triangle. [br][/b][/color][i]Hint: Solve for Sin A. [br][/i][br]We have, [br][math]sinA=\frac{h}{c}[/math] [i]cross multiply, we get[br][/i][br][math]cSinA=h[/math][br][br]Now, tick the second box. Use the [b]sine function [/b]to find the length of [b]h[/b] in the [color=#ff7700][b]orange triangle.[/b] [br][/color][i]Hint: Solve for Sin C. [/i]
Eliminate [b]h [/b]in your answers by equating them together. [br][math]cSinA=aSinC[/math][b][br]Divide both sides by [color=#ff00ff]ac[br][br][/color]What do you get?[br][br][/b]
Refer to Triangle ABC above. The third box is done for you. [br][br]Tick the third box. [br]We can use the sine function to find an expression for [b]k[/b] in the [color=#38761d][b]green triangle. [/b][br][/color][i]Hint: Solve for Sin B. [br][/i][br]We have, [br][math]sinB=\frac{k}{c}[/math] [i]cross multiply, we get[br][/i][br][math]cSinB=k[/math][br][br]Now, tick the fourth box. Use the [b]sine function [/b]to find the length of [b]k[/b] in the [color=#0000ff][b]blue triangle. [/b][br][/color][i]Hint: Solve for Sin C. [/i]
Eliminate [b]k [/b]in your answers by equating them together. [br][math]cSinB=bSinC[/math][b][br]Divide both sides by [color=#ff00ff]bc[br][br][/color]What do you get?[br][br][/b]
The proportion that you just made is what we call the Law of Sines.
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[/img]
Now, let us observe the law of sines in action. Tick the boxes A, B, and C to show its ratios. Observe what happens.
Adjust the values of the angles and the sides by sliding the points A, B, C. [br][br]What happens to the ratio of any side length to the sine of the angle opposite that side? [br][br]Is this true for all?
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Information: Math 9 - Sine Law