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Warm Up #1

Warm Up #2

City of Atlanta

Solution

Extension Assignment (HW)

DERIVED FROM THE ANCIENT

GREEK LANGUAGE AND MEANS THE

MEASUREMENT OF TRIANGLES.

Trigonometry

Measurement of Triangles

Sides

Ways we already know:

Pythagorean TheoremCongruent Triangles Similar Triangles

Angles

Ways we already know:

Triangle Sum TheoremCongruent TrianglesSimilar Triangles

Vocabulary we need…

Vocabulary we need…

Labeling a right triangle

For any right triangle , six ratios of pairs of sides are possible.

b a b c , , , , ,

c b a b

a c

c a

This year we will study 3 of the ratios.

Sine ratioThe sine of A …

The sine of B …

length of side opposite Asin( )

length of hypotenuse

aA

c

length of side opposite sin( )

length of hypotenuse

B bB

c

Ex.1 In ∆ ABC, find the following…

sin( )A

sin( )B

8

1715

17

The cosine of A …

The cosine of B …

length of side adjacent to Acos( )

hypotenuse

bA

c

length of side adjacent to cos( )

hypotenuse

B aB

c

Cosine ratio

Ex.2 In ∆ ABC, find the following…

cos( )A

cos( )B

15

17

8

17

The tangent of A …

The tangent of B …

length of side opposite tan( )

length of side adjacent

B bB

B a

length of side opposite Atan( )

length of side adjacent A

aA

b

Tangent ratio

Ex.3 In ∆ ABC, find the following…

tan( )A

tan( )B

8

15

15

8

A little help to remember….

SOHCAHTOASOH - Sine , Opposite leg,

HypotenuseCAH - Cosine , Adjacent leg,

HypotenuseTOA - Tangent, Opposite leg,

Adjacent leg

Let’s practice…

Using angle measures

Since corresponding sides of similar triangles are proportional, the sine ratio is the same in any right triangle. This is true for any trigonometric value of an angle in a right triangle. The values for any angle measures can be found using a calculator.

sin

sin

A

D

CalculatorsMake sure that your

calculator is in degree mode sin 43

tan57

cos71

0.6820

1.5399

0.3256

You can find the measure of an angle if one of its trigonometric values is known.

Example 1 :

Example 2:

1

cos 0.5592

cos (0.5592)

A

1

2sin

32

sin3

A

Guided Practice

Making Practice Fun 82

Solving Right Triangle Problems

In ∆ ABC , m<B = 61°, c = 20, find b.

b = 17.5

Solving Right Triangle Problems

In ∆ ABC , m<B = 42°, c = 10, find b.

b = 6.7

Solving Right Triangle Problems

In ∆ ABC , m<A = 39°, b = 20, find a.

a = 7.3

Finding an angle measure

Find the m<A?

What trig function?

23.9°

Angle of Elevation/ Angle of Depression

The angle of elevation of an airplane is 12°. The distance to the plane is 16 km. How high is the plane?

3.3 km

A fire warden’s tower is 43 m tall. The angle of depression from the window of the tower to a fire in the woods is 5°. How far away from the base of the tower is the fire?

491 m

Guided practice

1. A kite is flown with 210 m of string. The angle of elevation of the kite is 61°. How high is the kite?

2. The top of a lighthouse is 110 m above the level of the water. The angle of depression from the top of the lighthouse to a fishing boat is 18°. How far is the base of the lighthouse is the fishing boat?

3. A mountain trial slopes upward at an angle of 5°. A hiker hikes four miles up the trail. How much altitude does the hiker gain?

187.3 m 338.6 m 0.35 km

Assignment

Making Practice Fun 83

“Big Grass Field” Puzzle