Drill

Find the missing side length of right triangle ABC. Assume side C is the hypotenuse.

1.A = 7, B = 32.A = 9, C = 15

Section 4.2

Students will calculate trig ratios.

What is Trig?

• Based on similar triangles• Used to find an unknown angle or

side length of a triangle• Uses ratios

Trig Functions

A

c b

B a C

The six trig ratios:

oppsine θ = sin θ =

hyp

opptangent θ = tan θ =

adj

adjcosine θ = cos θ =

hyp

hypcosecant θ = csc θ =

opp

hypsecant θ = sec θ =

adj

adjcotangent θ = cot θ =

opp

Just Remember:

• SOH CAH TOA

• It means: – Sin = opp/hyp– Cos = adj/hyp– Tan = opp/adj

Find the six trig ratios of angle A in the following right

triangle.

A

12

B 8 C

4 13

Calculate the six trig ratios of angle A and angle C in

the following right triangle.

A

4 5

B 3 C

Special Right Triangles

• 30-60-90

x√3 2x

x

30

60

Find all sides, then calculate six trig ratios of angle A.

A 30

60

B 5 C

Special Right Triangles

• 45-45-90

A

x x√2

B x C

Find all sides, then calculate six trig ratios of angle A.

12

A

B C

Use your calculator to calculate:

• sin 65°• cos 125°• tan 15°• sec 325°• csc 230°• cot 212°

Use your calculator to calculate

• sin

• cos

• tan

• csc

• sec

• cot

37

15

213

59

67

35

Example

• Let Ө be an acute angle such that sin Ө = 5/6. Evaluate the other five trig functions of Ө .

Example

• Let Ө be an acute angle such that sec Ө = 12/5. Evaluate the other five trig functions of Ө .

Solve the right triangle ABC for all of its unknown parts.

• A = 20 degrees, a = 12.3• B = 55 degrees, a = 15.58• A = 35 degrees, c = 15• B = 48 degrees, b = 7

C

A

B

Evaluate without using a calculator

1.sin 4. csc

3 4

2.cos 5. sec3 6

3.tan 6. cot 4 6

Problem Solving with Trig

• An angle of elevation is the angle through which the eye moves up from horizontal to look at something above.

Angle of Elevation

Problem solving

• An angle of depression is the angle through which the eye moves down from horizontal to look at something below. Angle of depression

Example

• From a point 340 feet away from the base of the Peachtree Center Plaza in Atlanta, Georgia, the angle of elevation to the top of the building is 65 degrees. Find the height of the building.

Example

• The angle of depression of a buoy from the top of a lighthouse 130 feet above the surface of the water is 6 degrees. Find the distance from the base of the lighthouse to the buoy.

Example

• A tree casts a shadow 51 feet long when the angle of elevation of the sun (measured with the horizon) is 25 degrees. How tall is the tree?

Homework

• Read 4.2, do #s 1 – 53 odd, 61, 65