13)+Use+Law+of+Sines+to+solve+triangles

=media type="file" key="Law of sines.mp4"Using Law of Sines to Solve Triangles= By Brandon Casey Period 1

Background: Doing law of sines in class was challenging, but once you do it enough it becomes easy and a fast way to solve triangles. It avoids simple trig and in my opinion makes solving triangles more understandable. In a way it was difficult, but using the formula for law of sines involves algebra which i would prefer over geometry.

Explanation: Using law of sines to solve triangles is a simple way to find lengths and angles in a triangle. The formula for law of sines is: **sinA/a=sinB/b=sinC/c** To use this formula, you plug in an angle measurement in a capital letter. Then you would divide that by the side length opposite to the angle above it. If there is an unknown, leave it be until the formula is filled in and you can then solve for it. In the picture below, the uppercase letters represent a give angle and the lowercase letters represent a given side length. To apply this formula to solving triangles, you simply plug in an angle/side length of a certain side and solve the remaining equation for the unknown value which could be either a side length or angle.

Examples: In this example, say a=3, B=60 degrees, and b=5 To solve use the law of sines formula, plug in the values, and solve for the unknown. sin60/5=sinx/3 Then: 3sin60/5=sinx Next: take the inverse sin of 3sin60/5 X=31.307 degrees In this example, make A=60, B=40, and c=5 To solve: C=80 degrees because 180-(60+40)=80 Then use the formula: sin80/5=sin40/x Solve for x: x=3.264

Example 3: solve the whole triangle (based on the previous pictures) when a=12.2 b=10 and A=75 First, you must find the angles inside the triangles... sin75/12.2=sinx/10 10sin75/12.2=sinx x=52.35 Then find the third angle... 75+52.35=127.35 180-127.35=52.65 Then find the third side... sin75/12.2=sin52.65/x x=10.04

Final Problem: You wants to buy land for his business. The land is the shape of a triangle and he knows only little dimensions. The land costs $150 per 100 feet squared. How much will it cost you to buy the land? Solve using law of sines.

Dimensions: A triangle, a=50 feet, b=75 feet, B=70 degrees