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```Right Triangle Ratios
1. In the following triangles, find the length of the hypotenuse.
x
4 ft.
x
12 in.
36˚
7 in.
2. How many side lengths of the right triangle must you know to be able use the Pythagorean Theorem?
3. Trigonometry is what you use when you can’t use the Pythagorean Thm. Here is what you need to know to use
Trig.
a. One acute angle measure
b. One side of the right triangle
4. Trigonometry is based on ratios. The ratios are developed by comparing sides of the right triangle based on
their location compared to the acute angle. Look at the illustration below.
Example 2
Hypotenuse
38˚
Hypotenuse
Opposite Leg
Example 1
38˚
Opposite Leg
Look at the right triangle below and finish completing the ratios by filling in the missing numbers
Adjacent Leg = 12 = 3
Hypotenuse
20
5
Opposite Leg = ____ = _____
Hypotenuse
20
20 ft
16 ft
Opposite Leg = _____ = ______
24˚
12 ft
Complete the ratios for the given triangles using the given angle, α (Theta). Some of these triangles are similar. As you
complete the trigonometry ratios, decide which triangles are similar and list them in the table on the following page. Not
drawn to scale
H
D
C
13
5
4√5
12
α 16
α
8
α
A
P
T.
8
O
12
O
G
8√3
Opp. Leg
= ______
Opp. Leg
= ______
Opp. Leg = ______
Hypotenuse
Hypotenuse
Hypotenuse
Hypotenuse
= ______
Hypotenuse
= ______
Hypotenuse
= ______
Opp. Leg
= ______
Opp. Leg
= ______
Opp. Leg
= ______
N
B
B
48
24
α
4
α
T
9
α
E
24√ 3
26
10
T
Opp. Leg
Hypotenuse
= ______
Hypotenuse
= ______
Opp. Leg
= ______
D
A
8
Opp. Leg
Hypotenuse
I
24
= ______
Opp. Leg = ______
Hypotenuse
Hypotenuse
= ______
Hypotenuse
= ______
Opp. Leg
= ______
Opp. Leg
= ______
W
L
C
α
12
N
α
√985
29
√410
11
8
18
A
G
O
17
Y
α
16
Opp. Leg
Hypotenuse
= ______
Opp. Leg
Hypotenuse
= ______
Opp. Leg = ______
Hypotenuse
Hypotenuse
= ______
Hypotenuse
= ______
Hypotenuse
= ______
Opp. Leg
= ______
Opp. Leg
= ______
Opp. Leg
= ______
H
Write the names of the similar triangles, using the vertices, from the previous page in the table below
Triangle 1
Example
CAT
is similar ~
Triangle 2
DOG
5. These ratios have special names that match several keys on your calculator
Sine Ratio (SIN) is Opposite Leg (of acute angle)
Hypotenuse
Cosine Ratio (COS) is Adjacent Leg (to acute angle)
Hypotenuse
Tangent Ratio (TAN) is Opposite Leg