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***Make sure your calculator is in DEGREE mode
Triangle Trigonometry
Name
Period #
Definition 1: ____________________ means triangle measurement.
*The relationships among the angle measures and side lengths of triangles are important building blocks used
in surveying, engineering, and architecture.
Definition 2: The ratio of the lengths of two sides of a right triangle is called a
_________________________________ ratio.
SOH-CAH-TOA
=
length of leg opposite A
length of hypotneuse
cos A
=
length of leg adjacent to A
length of hypotneuse
tan A
=
length of leg opposite A
length of leg adjacent to A
sin A

a
c
A

b
c
b

a
b
C
c
B
a
Ex 1: For ΔXYZ, find the sine, cosine, and tangent of  X .
sin X =
cos X =
16
X
20
tan X =
The RECIPROCAL TRIG FUNCTIONS of the primary ratios also have special names …
6
13
sin X =
csc X =
(cosecant)
13
6
13
9
13
Y
cos X =
sec X =
(secant)
13
9
6
2
3
9
tan X =
cot X =
(cotangent)
3
2
Z
Y
12
Z
X
2) Find the sine, cosine, tangent, cosecant, secant, and cotangent of X in ΔXYZ. If necessary, round these
values to the nearest thousandth.
X
First, you need to find y:
80
Y
y
150
sin X =
cos X =
tan X =
csc X =
sec X =
cot X =
Z
If you know the measure of an acute angle, you can use a calculator to find its sin, cos, or tan ratio. These
ratios can help you solve problems involving side lengths in right triangles.
3) A 12-ft ladder is placed against a building so that the ladder makes an angle of 50 degrees with the ground.
(Hint: ALWAYS draw figures if possible!)
a) To the nearest tenth of a foot, at what height does the ladder touch the building?
b) How far from the base of the building is the foot of the ladder?
Definition 3: An angle of _____________________ or angle of _____________________ to an object is
formed by the line of sight and a horizontal line.
*The ____________________ of the angle is the eye of the person looking at the object.
If two sides of a right triangle are known, then measures of the acute ANGLES can be found using the
INVERSE keys on your calculator.
4) An airplane is headed for Chicago’s O’Hare airport, 12.5 miles away. If the airplane is at an altitude of 5
miles, what is the angle of depression, to the nearest degree, from the airplane to the airport.
(Hint: DRAW it out!!!)
***Make sure your calculator is in DEGREE mode
Triangle Trig Practice Worksheet 1
Name
Period #
Refer to right triangle MLK .
1) What is the length of the leg opposite L ?
_______________
2) What is the length of the leg opposite K ?
M
3) What is the length of the side adjacent to L ?
5
4) What is the length of the side adjacent to K ?
K
12
13
L
_______________
_______________
_______________
5) Fill in the blanks below using KLM :
a) sin K 
b) cos L 
c) tan K 
d) sec L 
Match the name of each trigonometric ratio with the correct ratio of side lengths of a right triangle.
opposite
_________ 6) SINE
a)
adjacent
hypotenuse
_________ 7) COSINE
b)
opposite
adjacent
_________ 8) TANGENT
c)
hypotenuse
adjacent
_________ 9) COSECANT
d)
opposite
opposite
_________ 10) SECANT
e)
hypotenuse
hypotenuse
_________ 11) COTANGENT
f)
adjacent
B
Use ABC to find each trigonometric ratio IN SIMPLEST FORM.
12) sin A = _________
13) cos A = _________
14) tan A = _________
15) sin B = _________
16) cos B = _________
17) tan B = _________
39
A
15
36
C
18) The shadow of a flagpole is 16 feet at the same time that a 6-foot person casts a 4-foot shadow. How tall is
the flagpole? (HINT: Draw it!!!)