Math 109

Trigonometric Ratios

Examples of the Trigonometric Ratios

1)

Find

2)

Find

Evaluating the trigonometric of degree measures

Examples

Use a calculator or the tables on pages 465 and 471 in the textbook

Find the missing sides x and y

1)

2)

3)

20)

Find the missing angles and

1)

2) Find the missing angles and

Applications of Trigonometric Functions

Page 468-469

28)

30) Over a 2000 ft span of highway through a hillside, there is a 100 ft rise in the roadway. What is the measure of the angle formed by the road and the horizontal?

32) A 12 foot rope secures a row boat to a pier that is 4ft above the water. What is the angle of formed by the rope and the water?

Page 475

30) Gene redesigned a garage so that 12 ft roof would rise 2 ft as shown. Find the measure of angle θ.

32)

From a point 200 ft from the base of a cliff, the top of a cliff is seen through an angle of elevation of 37°. How tall is the cliff?

Other examples

1) Roadrunner is standing at the top of a 100 ft cliff looking at Wile E Coyote. If the angle of depression is 25°, how far is the roadrunner form the coyote?

Trigonometric Relationships

Using the sine ratio to find the area of a triangle

Using the area of a triangle formula will give the following equation.

The same arguments can be made using and to get the similar formulas.

As a result there is three formula to find the area of a triangle given two sides and and included angle.

Examples

1) Find the area of the triangle give two sides and an angle.

2)

Law of Sines

Examples

1) Find side b using the law of Sines.

Page 495

18)

22)

Law of Cosines

Law of Cosines (In an acute triangle)

Examples

1)

2) Find x

3) Find c