Wednesday: Warm-up• Draw a unit circle and label

all the key angles in degrees.

• You also need a calculator for today!

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Right Triangle Trigonometry

Section 4-3

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Objectives

• I can use Special Triangle Rules• 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.

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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

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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

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Calculator Mode

• MUST be set to DEGREES!!

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Finding an Angle

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We have the opposite side and hypotenuse

Sin θ = 2/5

= sin-1(2/5) = 23.58°

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Word Problems

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

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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.

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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

4242tan16

d

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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(14/16) = 61.044975

The painter’s plan is unsafe!

ladderhouse1614

The angle formed by the ladder and the ground is 61.04

θsin =

16

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Homework

• WS 8-1

• Study Special Triangle values