Section 4-3
Right Triangle
Trigonometry
Objectives
• I can use Special Triangle Rules
• I can identify how the 6 trig functions
relate to the memory aide SOH-CAHTOA
• I can use SOH-CAH-TOA to find
information from right triangles and word
problems
2
Special Right Triangles
30o, 45o, 60o
60o
You must
memorize
these!!!
1
2
3
2
3
2
The x-value is the
cosine of that
angle.
2
2
2
2
2
2
The y-value is the
sine of that angle.
Use the pythagorean theorem to find the sides.
1
2
The six trigonometric functions of a right triangle, with an acute
angle , are defined by ratios of two sides of the triangle.
The sides of the right triangle are:
hyp
 the side opposite the acute angle ,
opp
 the side adjacent to the acute angle ,
θ
 and the hypotenuse of the right triangle.
adj
Memory Aide: SOH-CAH-TOA
sine, cosine, tangent, cotangent, secant, and cosecant.
opp
sin  =
cos  = adj
tan  = opp
hyp
hyp
adj
csc  =
hyp
opp
sec  = hyp
adj
cot  = adj
opp
4
Calculate the trigonometric functions for  .
5
4

3
The six trig ratios are
4
sin  =
5
4
tan  =
3
5
sec  =
3
3
cos  =
5
3
cot  =
4
5
csc  =
4
5
Calculator Mode
• MUST be set to DEGREES!!
6
Finding an Angle
5
2

We have the opposite side and hypotenuse
Sin θ = 2/5
 = sin-1(2/5) = 23.6°
7
Word Problems
• Always draw a picture or
diagram to represent the
situation.
8
Angle of Elevation and Angle of Depression
When an observer is looking upward, the angle formed
by a horizontal line and the line of sight is called the:
angle of elevation.
line of sight
object
angle of elevation
horizontal
observer
When an observer is looking downward, the angle formed
by a horizontal line and the line of sight is called the:
horizontal
angle of depression
line of sight
object
observer
angle of depression.
9
Example 2:
A ship at sea is sighted by an observer at the edge of a cliff
42 m high. The angle of depression to the ship is 16. What
is the distance from the ship to the base of the cliff?
observer
cliff
42 m
horizontal
16○ angle of depression
line of sight
16○
d
ship
42
= 146.47.
tan 16
The ship is 146.47 m from the base of the cliff.
d=
10
Example 3:
A house painter plans to use a 16 foot ladder to reach a spot
14 feet up on the side of a house. A warning sticker on the
ladder says it cannot be used safely at more than a 60 angle
of inclination. Does the painter’s plan satisfy the safety
requirements for the use of the ladder?
ladder
house
14
16
sin  =
= 0.875
14
16
θ
Next use the inverse sine function to find .
 = sin1(0.875) = 61.044975
The angle formed by the ladder and the ground is about 61.
The painter’s plan is unsafe!
11
Homework
• WS 6-4
12