Law of Sines: Intro via Areas

In the app below, points A and B are MOVEABLE. You can change the sizes of the colored angles using the two colored sliders in the lower left corner. Slide the long slider slowly and carefully watch what happens!

[img width=329,height=170]https://lh6.googleusercontent.com/MP__fZu80x1doBPReABsDuZddxJj0leoUvgMv70UrxfEpTMWH9GP7HKvIVpedWo1Fyc3Ww1ZrdCLY_l4LOa_nxirCJsGmRChdt3jwP0dIWAhks2_yvuMJNsWCI-bWRyHQi1iLETo[/img][br][br][br][br]What is the area of this rectangle in terms of [i][b]a[/b][/i] and [i][b]sin B[/b][/i]?

[img width=236,height=220]https://lh5.googleusercontent.com/bGoknLi6GkA-yFtCKiWWaplR8IH6-_ixHn8_hZ6X8wFAnQb1m50pMbqd-fa6EEGAFPSYF3nJAM4DJQSNbGAQRO9HBqLUqf1ac0iWUhGBTpw9ZAkDUjXUlOVK35Uu7hCjGozYBNK6[/img][br][br][br][br][br][br][br]What is the area of this rectangle in terms of[b] [i]b[/i] [/b]and [b][i]sin[/i] [i]A[/i][/b]?

What can we conclude about the areas of these two rectangles? Why can we conclude this?

Given your responses to the questions above, write an equation that expresses the relationship among [b][i]a[/i], [i]b[/i], sin [i]A[/i], and sin [i]B[/i]. [/b]

Copy the equation you wrote above in the app below. Then rewrite an equivalent equation so that a and sin(A) appear on one side of the equation and so b and sin(B) appear on the other side.

Law of Sines: Intro via Areas

In the app below, points A and B are MOVEABLE. You can change the sizes of the colored angles using the two colored sliders in the lower left corner. Slide the long slider slowly and carefully watch what happens!

Copy the equation you wrote above in the app below. Then rewrite an equivalent equation so that a and sin(A) appear on one side of the equation and so b and sin(B) appear on the other side.

Quick (silent) demo

Information: Law of Sines: Intro via Areas