Equations and Trig Ratios
SOH, CAH, or TOA?
Missing Sides
Creating Equal Ratios
Theorems & Theories
100
Ratio of sine
opposite/hypotenuse
100
Label each side as Opposite, Adjacent, or Hypotenuse using angle Y at a reference.
a = adjacent, b= opposite, c= hypotenuse
100
Angle y = 62 degrees and a = 3, what does b equal?
tan(62) = b/3
b = 5.64
100
Are these two triangles similar? Why or why not? Use a theorem we talked about to answer properly
No because they need at least two angles in common and these only have one (90). This is the Angle-Angle similarity theorem.
100
What are our four transformations? Which of those 4 are rigid transformations?
Translate (rigid); Rotate (rigid); Reflect (rigid); dilation
200
Ratio of Tangent
opposite/adjacent
200
if b = 20, and <X = 35, would I use SOH, CAH, or TOA, to solve for C.
CAH (cosine)
200
If angle x = 65 degrees and c = 11, what does b equal
cos(65) = b/11
b = 4.65
200
What ratio equals EF/DE
ST/SR
200
What do you call two angles that add up to equal 90 degrees?
Complimentary angles.
300
Ratio of Cosine
cos(x) = A/H
300
If <x = 45 degrees, and c = 35, would I use SOH, CAH or TOA to find side a
SOH, (sine)
300
Angle = 37 degrees, opposite leg = 17.3. Find the hypotenuse.
Round to nearest tenth (0.0)
sin(37) = 17.3/h
h = 28.297 or 28.3
300
c/b =
f/e
300
Triangle Sum Theory
The all the angle measurements in a triangle will have a sum of 180 degrees
400
What would make this value true:
cos(6) = sin(x)
x = 84
400
Set up the trig ratio I would use if I had angle Y and was comparing side b and side a
TOA, tan(y) = B/A
400
If angle Y= 35 degrees and side c = 40, what is the length of side a?
cos(35) = a/40
= 32.77
400
The ratio PQ/QR is equal to what ratio in ABC?
AB/BC
400
Angle-Angle Similarity Theorem.
If two triangles have two pairs of congruent corresponding angles, then those two triangles are similar.
500
A 40ft flag pole has a rope tied from the top to the ground. The rope makes a 25 degree angle with the ground. Set up the trig equation to find the length of the rope
sin(25) = 40/H
500
Set up SOH, CAH, and TOA for angle X. (Must list all three)
SOH = sin(A) = a/c,
CAH = cos(a) = b/c
TOA = tan(a) = a/b
500
2 STEP: If angle X is 45 degrees, and b is 5, how long are both A and C. (must find both)
cos(45) = 5/c --> c = 7.07
sin (45) = a/7.07 --> a = 4.99 (or 5)
500
Set up a proportion (two equal ratios) to find x.
2/3 = 8/x
2/8 = 3/x
500
What are our three congruence conjectures?
Side-Angle-Side
Angle-Side-Angle
Side-Side-Side