Right Triangle Trigonometry

Section 4-3

2

Objectives

• I can use Special Triangle Rules

• I can identify how the 6 trig functions relate to the memory aide SOH-CAH-TOA

• I can use SOH-CAH-TOA to find information from right triangles and word problems

Special Right Triangles 30o, 45o, 60o

1

22

2

3

2

60o

Use the pythagorean theorem to find the sides.

3

2

2

2

2

21

2

You must memorize these!!!

The x-value is the cosine of that angle.

The y-value is the sine of that angle.

4

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:

the side opposite the acute angle ,

the side adjacent to the acute angle , and the hypotenuse of the right triangle.

Memory Aide: SOH-CAH-TOA

sine, cosine, tangent, cotangent, secant, and cosecant.

opp

adj

hyp

θ

sin = cos = tan =

csc = sec = cot =

opphyp

adj

hyp

hypadj

adj

opp

oppadj

hyp

opp

5

Calculate the trigonometric functions for .

The six trig ratios are

4

3

5

sin =5

4

tan =3

4

sec =3

5

cos =5

3

cot =4

3

csc =4

5

6

Calculator Mode

• MUST be set to DEGREES!!

7

Finding an Angle

25

We have the opposite side and hypotenuse

Sin θ = 2/5

= sin-1(2/5) = 23.6°

8

Word Problems

• Always draw a picture or diagram to represent the situation.

9

angle of elevation

When an observer is looking downward, the angle formed by a horizontal line and the line of sight is called the:

Angle of Elevation and Angle of Depression

When an observer is looking upward,

angle of elevation.

the angle formed by a horizontal line and the line of sight is called the:

observerobjectline of sight

horizontal

observer

objectline of sight

horizontal

angle of depressionangle of depression.

10

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?

The ship is 146.47 m from the base of the cliff.

line of sight

angle of depressionhorizontalobserver

ship

cliff42 m

16○

16○

d

d = = 146.47. 16tan

42

11

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 angleof inclination. Does the painter’s plan satisfy the safetyrequirements for the use of the ladder?

Next use the inverse sine function to find .

= sin1(0.875) = 61.044975

The painter’s plan is unsafe!

ladderhouse1614

The angle formed by the ladder and the ground is about 61.

θsin = = 0.875

16

14

12

Homework

• WS 6-4