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13-1 Right Triangle Trigonometry
Trigonometry:
* The study of the relationship among
the angles and sides of a right triangle.
B
hypotenuse
A leg opposite of B
leg adjacent to A
leg opposite of A
leg adjacent to B
C
Trigonometric Functions:
* Ratios that use the sides of a right
triangle.
sine (sin)
cosine (cos)
tangent (tan)
cosecant (csc)
secant (sec)
cotangent (cot)
opp
= hyp
csc
cos =
adj
hyp
sec
tan =
opp
adj
cot
sin
hyp
= opp
hyp
=
adj
=
adj
opp
Special Right Triangles:
30˚- 60˚- 90˚ and 45˚ - 45˚ - 90˚
Domain of each trig. function is the set of
all acute angles of a right triangle.
0 < < 90
You can use one trig. ratio to find the value
of another.
Always use what you are given when
trying to solve a right triangle.
30˚
2x
x√ 3
x
45˚
x√2
45˚
60˚
x
x
Solving a Right Triangle:
* When you know two sides of a right
triangles or one side and an acute angle,
then you can find the measures of all of
the sides and angles.
angle of depression
Angle of Elevation:
* The angle we look up at.
line of sight
Angle of Depression:
* The angle we look down from.
angle of elevation
Line of Sight:
* The path that our eyes follow.
1. Find the values of the six trig. functions for
angle G.
H
32
24
F
3. Write an equation involving sin, cos, or tan
that can be used to find the value of x.
Then solve the equation. Round to the
nearest tenth.
40
x
G
12
60˚
2. If tan A =
5
, find the value of csc A.
3
4. Solve ∆XYZ. Round measures of sides
to the nearest tenth and measures of
angles to the nearest degree.
Y
Z
11
28˚
X
5.
In order to construct a bridge across a river, the width of
the river at that location must be determined. Suppose a
stake is planted on one side of the river directly across
from a second stake at the opposite side. At a distance
30 meters to the left of the stake, at an angle of 55˚ is
measured between the two stakes.
13 - 1 Right Triangle Trigonometry
p. 706 - 708
#13, 15, 16, 22, 24, 26, 30, 32, 34, 35, 38,
41 - 42, 49, 50, 56, 58
(17 problems)
6. A run has an angle of elevation of 15.7˚
and a vertical drop of 1,800 feet.
Estimate the length of the run.