SOHCAHTOA BY: KAYLA SLEDGE
Example
Pythagorean Theorem
The longest side of the triangle is called the "hypotenuse", so the formal definition is: In a right angled triangle:
the square of the hypotenuse is equal to
the sum of the squares of the other two sides.
a2 + b2 = c2
92 + b2 = 152
81 + b2 = 225
Take 81 from both sides:
b2 = 144
b = √144
b = 12
Inverse of Sine, Cosine, and Tangent
First, regardless of how you are used to dealing with exponentiation we tend to denote an inverse trig function with an “exponent” of “-1”. In other words, the inverse cosine is denoted as
cos a° = Adjacent / Hypotenuse
cos a° = 6,750/8,100 = 0.8333...
a° = cos-1 (0.8333...) = 33.6° (to 1 decimal place)
It is important here to note that in this case the “-1” is NOT an exponent and so,
tan x° = Opposite / Adjacent
tan x° = 300/400 = 0.75
x° = tan-1 (0.75) = 36.9° (correct to 1 decimal place)
Start with: sin a° = opposite/hypotenuse = 18.88/30
Calculate 18.88/30: sin a° = 0.6293...
Inverse Sine: a° = sin-1(0.6293...)
Use a calculator to find sin-1(0.6293...): a° = 39.0° (to 1 decimal place)
The angle "a" is 39.0°
Example
SOHCOHTOA
SOH - stands for Sine equals Oppisite over Hypotenuse
COH - stands for Cosine equals Adjacent over Hypotenuse
TOA - stands for Tangent equals Opposite over Adjacent
sin θ = 3/5 = 0.6
cosθ = 4/5 = 0.8
tanθ = 3/4 = 0.75