Geometry—Trig Notes & Review for Quiz #4
Name: ______________________________
Adjacent and Opposite Legs
Triangle JLK is a right triangle. ∠ J = θ
J
Θ = a Greek symbol usually representing an angle measure
25
Opposite Leg to Θ:
7
Adjacent Leg to Θ:
K
Hypotenuse:
Example 1: Identify the opposite and adjacent legs to ∠B.
Opposite Leg:
Adjacent Leg:
Hypotenuse:
L
24
Practice: Identify the opposite and adjacent legs to ∠Z.
A
X
Opposite Leg:
13
5
17
Adjacent Leg:
C
8
Z
Hypotenuse:
B
12
15
Example 3:
sin A = _____
cos A = _____
Y
SOH CAH TOA
tan A = _____
sin B = _____
cos B = _____
tan B = _____
B
5
A
3
4
C
Example 3: Find each trigonometric ratio for the given right
triangle.
Practice: Find each trigonometric ratio for the given right
triangle.
X
sin Z = ______
cos Z = ______
8
Z
tan Z = ______
A
sin A = ______
17
Y
15
cos A = ______
tan A = ______
C
Practice: Find each trigonometric ratio for the given right
triangle.
24
36
sin 𝜃 = ______
sin 𝜃 = ______
15
cos 𝜃 = ______
𝜃
hyp 𝜃= ______
B
12
Example 4: Find each trigonometric ratio for the given right
triangle.
cos 𝜃 = ______
13
5
39
hyp 𝜃= ______
𝜃
7
Example 5: An angle in a right triangle has a measureΘ.
12
If sinΘ = , then tanΘ = ?
13
Practice: An angle in a right triangle has a measure Θ.
8
If tanΘ = , then sin Θ = ?
15
Summary Review
Sine = ______________
Cosine = _______________
1. What does SOHCAHTOA stand for?
S
O
H
C
A
H
T
O
A
Tangent = ______________
2. Why do we memorize it?
3. Does SOHCAHTOA apply to all triangles?
3. Does SOHCAHTOA apply to all triangles?
5. List the four most common Pythagorean Triples.
6. Why is it helpful to have these Pythagorean Triples
memorized?
Challenge Problems
1. Find each trigonometric ratio.
5. Find each trigonometric ratio.
B
c
(0, 1)
a
A
C
b
Θ
(1, 0)
sin Θ = ______
sin A = ______
sin B = ______
cos A = ______
cos B = ______
tan A = ______
tan B = ______
cos Θ = ______
tan Θ = ______
6. In the figure below, ∠C is a right angle, and a, b, and c
represent the lengths of the sides of the right triangle. What is
the cosine of ∠A? What is the tangent of ∠B?
7. In the figure below, ⊿ ABC is a right triangle with a right angle
at C. Which of the statements about this figure is NOT correct?
A
A
a.
30
C
16
B
cos A =
b.
sin A =
c.
tan A =
d.
cos B =
e.
tan B =
3
5
4
5
5
3
3
4
4
5
3
4
C
B
4