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Basic Trigonometry

- Sine
- Cosine
- Tangent

The Language of Trig

The target angle is either one of the acute

angles of the right triangle.

Hypotenuse

Opposite

target angle

?

Adjacent

Trig Equations

Hypotenuse

Opposite

target angle

?

Adjacent

opposite

?

sin

Hypotenuse

Trig Equations

Hypotenuse

Opposite

target angle

?

Adjacent

?

Adjacent

COS

Hypotenuse

Trig Equations

Hypotenuse

Opposite

target angle

?

Adjacent

?

opposite

TAN

Adjacent

SOH - CAH - TOA

Given sides, find requested ratios

- Locate indicated angle and classify sides in

relation to it. - Use proper equation and write the ratio.
- Use calculator to round to the nearest

ten-thousandths place.

Hypotenuse

Opposite

Adjacent

Find sin, cos, and tan of ?A.

8.2

opposite

sin A

24.5

Hypotenuse

23.1

COS A

Adjacent

24.5

Hypotenuse

8.2

opposite

TAN A

23.1

Adjacent

Solving for the unknown

- Unknown on top..Multiply

x

sin 40

24

Calculator 24 (sin 40) 15.4

Solving for the unknown

- Unknown on bottom..Divide

24

sin 40

x

Calculator 24 ?(sin 40) 37.3

Solving for the unknown

- Unknown angle..use inverse

15.4

x

sin

24

Calculator 2nd sin-1 (15.4/24) 40

Solving problems using trig

- Choose your target angle and classify sides in

relation to it. - Use proper equation and write the ratio placing

the unknown wherever it falls. - SolveUnless directed otherwise, round sides to

nearest tenth and angles to nearest degree.

Hypotenuse

Opposite

sin

Opposite

Hypotenuse

h

sin 30

52.6

h 52.6(sin 30) 26.3

Angle of Elevation

The angle of elevation is always Measured from

the Horizontal UP It is always INSIDE the

triangle.

Angle of Depression

The angle of depression is always Measured from

the Horizontal DOWN It is usually OUTSIDE the

triangle.

x

?

?

However.because horizontal lines are parallel,

an angle of depression is equal to its alternate

interior angle of elevation.

Practice

h

opposite

TAN 67

h

Opposite

Adjacent

30m

67?

30m

Adjacent

h 30(tan 67)

70.7m

From a point on the ground 25 feet from the foot

of a tree, the angle of elevation of the top of

the tree is 32º. Find to the nearest foot, the

height of the tree.

Adj

Hyp

Opp

TAN

x ft

x ft

32

32

x ? 16 ft

25 ft

25 ft