8.1.4 – Areas of Non-Right Triangles

Using the idea behind the Law of Sines/Law of Cosines (working with non-right triangles, finding missing sides and or angles), we want to extend the idea to finding other information for non-right triangles One important one is the area of any triangle

General Area Formula Recall, the general area of a triangle is: (1/2) (base)(height) Another way to think of it is one-half the product of the lengths of any two sides

Sine Formula Sine Formula Area: Area = (1/2)abSin(C) Area = (1/2)bcSin(A) Area = (1/2)acSin(B)

Heron’s Formula Alternatively, we can find the area without any knowledge of angles Let s = (a+b+c)/2 Then: Area =

Cannot use Heron’s Formula without knowledge of all three sides If you know an angle, best to use the sine formula

Example. A person is considering purchasing a triangular piece of property. The property is enclosed by three roads. One road measures 147 feet, while a second measure 207 feet, with an included angle of 72 degrees. What is the area of the property?

Example. Bob is building a pretty sail for his boat. The bottom edge of the sail measures 7 feet, the vertical measures 11 feet, and the diagonal measures 12 feet. How much fabric does Bob need to create his sail?

Example. A garden is formed between a trio of sidewalks. One length of sidewalk measure 12 feet, while another measure 15 feet. If the included angle is 100 degrees, find the area of the enclosed garden.

Assignment Pg