Lawrence's blog

This week, we did chapter 9-1. It talked about solving for right triangles and law of sines.

Right triangle:
1. hypotenuse is opposite of the right angle
2. area= 1/2 base times height
3. SOH CAH TOA
-sin theta =opposite/hypotenuse
-csc theta=hypotenuse/opposite
-cos theta=adjacent/hypotenuse
-sec theta=hypotenuse/adjacent
-tan theta=opposite/adjacent
-cot theta=adjacent/opposite

Ex: In triangle ABC, angle A=28 degrees, angle C=90 degrees, side a=49, what is side b?

tan28degrees=40/b
btan28degrees=40

b=75.229

Ex: In triangle ABC, angle A=50 degrees, angle C= 90 degrees, side c=10, what is side a?

sin 50 degrees= a/10

=10 sin 50 degrees= a

a= 7.660

Law of Sines:

sinA/a = sinB/b = sinC/c

Law of sines is used when you know pairs in non-right triangles

To use the law of sines, you are setting up a proportion

Ex: in triangle ABC, angle A=115 degrees, side a=123, side b=16, what is angle B?

sin115 degrees/123 = sin theta/16

123sin theta=16sin115 degrees

sin theta=16sin115 degrees/123

theta =sin inverse (16sin115 degrees/123)

theta =6.771 degrees

Ex: in triangle ABC, angle A=30 degrees, angle B=15 degrees, side a=4, what is side B?

sin 30 degrees/4 = sin 15 degrees/x

x sin 30 degrees = 4 sin 15 degrees

x= 4 sin 15 degrees/ sin 30 degrees

=4 sin 15 degrees/ 1/2

x= 2.071