1. Introduction to Trigonometry Part 1

2. If you know 2 sides of a right triangle…
You can find the third side.
A² + B² = C²
B² = C² - A²
A² = C² - B² b C A a B

3. If you know 2 angles… You can find the missing angle.
ma = 180 - (90 + mb)
mb = 180 - (90 + ma) b C A a B

4. What if you know one side & one angle and you want to find the missing sides?
Now you need to use trigonometry!
First we have to learn some vocabulary.

5. Some vocabulary:
The hypotenuse (hyp) is the longest side of the triangle – it is always across from the right angle
The opposite (opp) is the side directly across from the reference angle
The adjacent (adj) is the side next to the reference angle

6. A picture always helps…
Let b be your reference angle
A is the adjacent side (next to the angle) b C A
B is the opposite side (across from the angle) B b
Next
C is always the hypotenuse
hyp
Longest
adj
opp
Across

7. But if we switch angles…
Now let a be your reference angle
A is the opposite (across from the angle) C A a
B is the adjacent (next to the angle) B
Across
C is always the hypotenuse
hyp
Longest
opp a
adj
Next

8. Let’s practice… label each side relative to the reference angle.

9. Trigonometry uses ratios of the sides
There are three sets of ratios for any triangle
sin…short for sine
cos…short for cosine
tan…short for tangent

10. So what are the formulas?
Sin is Opposite over Hypotenuse
Tan is Opposite over Adjacent
Cos is Adjacent over Hypotenuse
SOH
CAH
TOA

11. If you need more help in memorizing…
Soh-Cah-Toa
Some old horse Caught another horse Taking oats away.
Some old horse Caught another horse Trotting on asphalt.

12. Calculating a side if you know the angle
you know a side (adj) and an angle (25°)
we want to know the opposite side b C A
25°
B = 6

13. And one sin example find the length of side A
We have the angle and the hyp, and we need the opp b
C = 20 A
25° B

14. What are the steps for doing one of these questions?
Label the sides
Choose SOH, CAH, or TOA
Solve the equation for the unknown value
Does the answer make sense?