Section 7.4Trigonometry

Trigonometry• How can I find trigonometric ratios for right

triangles?

Trigonometry• About triangle measurements

• Uses ratios of sides of a triangle to describe an angle

• Sine, Cosine and Tangent

• Abbreviated as sin, cos and tan

Sides• Which side is adjacent to angle B? • Which side is opposite to angle B?• Where is the hypotenuse?

A

BC

c

b

a

Sine

A

BC

c

b

a

Cosine

A

BC

c

b

a

Tangent

A

BC

c

b

a

SOH-CAH-TOA• Memory device

With Numbers!• Find sin, cos, and tan for B

B

AC

135

12

With Numbers!• Find sin, cos and tan for A and B

A

BC

257

24

Homework• Worksheet

Trigonometry• How can I use trigonometry to solve triangle

problems?

Using SOH-CAH-TOA• Calculator • (typically 4 places, round to the nearest ten-

thousandth

• sin 45• cos 36• tan 23

Inverse Functions• Given the trig value, what is the angle measure?

• Inverse function on calculator (

• sin x = 0.8387

• cos x = 0.5000

• tan x = 0.5774

Examples

Example

Application• A plane is one mile above sea level when it begins

to climb at a constant angle of 3° for the next 60 ground miles. About how far above sea level is the plane after its climb?

Application• To guard against a fall, a ladder should make an

angle of 75° or less with the ground.

• A. What is the maximum height that a 20-foot ladder can reach safely?• B. How far from the building is the base of the ladder at

maximum height?

Homework• Worksheet