Introduction to TrigonometryPart 1
If you know 2 sides of a right triangle…
You can find the third side.A² + B² = C²B² = C² - A²A² = C² - B²
AC
B
a
b
If you know 2 angles…
You can find the missing angle.ma = 180 - (90 + mb)mb = 180 - (90 + ma)
AC
B
a
b
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.
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
A picture always helps…
Let b be your reference angle
AC
B
b
adjhyp
opp
bC is always the hypotenuse
A is the adjacent side (next to the angle)
B is the opposite side (across from the angle)
LongestNext
Across
But if we switch angles…
Now let a be your reference angle
AC
B
a
opphyp
adja
C is always the hypotenuse
A is the opposite (across from the angle)
B is the adjacent (next to the angle)
LongestAcross
Next
Let’s practice… label each side relative to the reference angle.
Trigonometry uses ratios of the sides
There are three sets of ratios for any triangle
sin…short for sinecos…short for cosinetan…short for tangent
So what are the formulas?
hyp
oppsin
hyp
adjcos SOH
adj
opptan
CAHTOA
Sin is Opposite over HypotenuseCos is Adjacent over HypotenuseTan is Opposite over Adjacent
If you need more help in memorizing…
Soh-Cah-ToaSome old horse Caught another horse
Taking oats away.Some old horse Caught another horse
Trotting on asphalt.
Calculating a side if you know the angle
you know a side (adj) and an angle (25°)we want to know the opposite side
adj
opptan
A C
B = 6
25°
b
80.2
647.0
625tan6
25tan
A
A
A
A
And one sin example
find the length of side A We have the angle and
the hyp, and we need the opp
hyp
oppsin
C = 20
25°
b
B
A 45.8
2042.0
2025sin20
25sin
A
A
A
A
What are the steps for doing one of these questions?
1. Label the sides
2. Choose SOH, CAH, or TOA
3. Solve the equation for the unknown value
4. Does the answer make sense?
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