9-4

We finished up and tested on Chapter 9 this week. Exams are next week so we will begin reviewing. One of the easiest sections in Chapter 9 for me was 9-4. It was about Law of Cosines. It is used when you don’t have a pair in a non-right triangle.

The formula is: (opposite leg)^2=(adjacent leg)^2 +(adjacent leg)^2-2(adjacent leg)(adjacent leg)cos(angle b/w)

EXAMPLE 1: Suppose two sides of a triangle have lengths 4cm and 8cm and the angle between them measures 140 degrees. Find the third side.
A). Draw your triangle and label it.
B). We know that 4cm and 8cm are our adjacent legs and 140 degrees is our angle . So plug these numbers into the formula – x^2=8^2 +4^2 -2(8)(4)cos140 degrees
C). Since everything is squared, you must find the square root. Square root everything and plug
it into your calculator.
D). Your answer is 11.4

EXAMPLE 2: In triangle ABC, a=8, b=6, and angle c=50 degrees.
A). Draw your triangle and label it.
B). We know that 8 and 6 are our adjacent legs and 50 degrees is our angle. So plug these numbers into the formula - x^2=8^2 +6^2 -2(8)(6)cos50 degrees
C). Square root everything and plug it into your calculator.
D). Your answer is 6.2

This section is pretty simple because if you don’t have a pair to use Law of Sines then you just use Law of Cosines. Then all you do is plug your numbers in and solve.