Download Trigonometric Ratios Remember: Chief Soh Cah Toa

12.1 Trigonometric Ratios
Trigonometry – The study of the relationship between sides and angles of triangles.
B
c
a
A
C
b
Refer to (right) ΔABC above:
Looking at A:
________ is the opposite leg
Looking at B:
________ is the opposite leg
________ is the adjacent leg
________ is the adjacent leg
________ is the hypotenuse
________ is the hypotenuse
Trigonometric Ratios
length of leg opposite ∠A
a
sine of ∠A=
or sin A=
length of the hypotenuse
c
cosine of ∠A=
length of leg adjacent ∠A
b
or cos A=
length of the hypotenuse
c
tangent of ∠A=
length of leg opposite ∠A
a
or tan A=
length of leg adjacent ∠A
b
Remember: Chief Soh Cah Toa
Geometry Lesson 12.1: Trigonometric Ratios
Page 1
Example 1: Find the sine, cosine, and tangent of each angle.
a) sin A = _____
cos A = _____
tan A = ____
B
5
3
sin B = ____
cos B = ____
tan B = _____
A
C
b) sin D = _____
sin E = ____
cos D = _____
tan D = ____
cos E = ____
tan E = _____
4
E
17
15
D
T
F
8
5
12
c) sin R = _____
cos R = _____
tan R = ____
S
sin S = ____
cos S = ____
tan S = _____
13
R
Example 2: Use a calculator to find each trigonometric ratio accurate to four decimal places.
a) sin 31 = __________
b) sin 20 = __________
c) sin 70 = __________
d) cos 31 = __________
e) cos 20 = __________
f) cos 70 = __________
g) tan 31 = __________
h) tan 20 = __________
i) tan 70 = __________
Geometry Lesson 12.1: Trigonometric Ratios
Page 2
Example 3: Find the missing measures in the following right triangles.
a)
b)
11 cm
15 cm
y
42
38
x
c)
d)
9 cm
23
w
49
z
12 cm
Example 4: At a distance of 36 meters from a tree, the angle from the ground to the top of the tree is
31. Find the height of the tree.
Geometry Lesson 12.1: Trigonometric Ratios
Page 3
Example 5: Find the length of the hypotenuse of a right triangle if an acute angle measures 20 and
the side opposite the angle measures 410 feet.
Example 6: A right triangle has legs of length 8 inches and 15 inches. Find the length of the
hypotenuse and the measures of the two acute angles.
Example 7: A right triangle has a leg of length 32 inches and hypotenuse of length 74 inches. Find
the length of the other leg and the measures of the two acute angles.
Homework: pp. 624 – 625 => 1 – 20
Geometry Lesson 12.1: Trigonometric Ratios
Page 4