Chapter 9

This week we completed chapter eight and began chapter nine. The beginning of chapter one is trigonometry; solving right triangles. Section 9-1 goes back to chapter seven ;using trigonometry functions, as well as Geometry. A few additional steps are included. One of the most helpful tips to remember when using right triangles is SOHCAHTOA.

Sine: opposite/hyp
Cosine:adjacent/hyp
Tangent: opposite/adjacent

You must also remember that almost triangles' angles add up to equal 180 degrees. There are also special triangles such as the 45/45 and 60/30 that should be remembered.

When looking for the sides of a triangle use either pythagorean theorem ; a^2+b^2=c^2 , or trigonometric functions.

EXAMPLE: in triangle DEF you are given measure of angie D which is 90 degrees, measure of angle E which is 12 degrees, and the length of side E which is 9.
In order to solve this triangle you must find the measure of angle F, and the lengths of sides d and f .

To find the missing angle we must remember that all triangles add to equal 180 degrees. We see that the sum of our given angles is 102. Right angles equal 90 degrees plus the 12 degrees of angle E equal 102. Subtract from 18o , E is equal to 78. Next we must find the sides. In order to find side f we use the trig function tan, opposite/adjacent, of the given 12 degrees.

Tan 12=9/f . Cross multiply and divide to get 42.3. Therefore the length of side f is 42.3.
You now have two options to find the last side. You can 1. Use pythagorean theorem, or 2. Use the trig functions again. It's best to use the trig function again just in case your first answer was wrong.

To find side d you take sine 12 =9/d. Again you cross multiply and divide and you get 43.3. That is the length of side d.

Angles : 90, 12, 78.
Sides: 9, 42.3, 43.3
Now you have solved triangle DEF.