Finding an angle.(Figuring out which ratio to use and

getting to use the 2nd button and one of the trig buttons. These are the

inverse functions.)

5.4 Inverse Sine, Cosine and Tangent

Ex. 1: Find . Round to four decimal places.

9

17.2

Make sure you are in degree mode (not radians).

9

2.17tan

2nd tan 17.2 9

3789.62

)

Ex. 2: Find . Round to three decimal places.

23

7

Make sure you are in degree mode (not radians).

23

7cos

2nd cos 7 23

281.72

)

Ex. 3: Find . Round to three decimal places.

400

200

Make sure you are in degree mode (not radians).

400

200sin

2nd sin 200 400

30

)

When we are trying to find a sidewe use sin, cos, or tan.

When we need to find an angle we use sin-1, cos-1, or tan-1.

Solve the right triangle. Round decimal answers to the nearest tenth.

“To solve a right triangle” means to find the measures of all of its sides and angles.

ANSWER The angle measures are 42o, 48o, and 90o. The

side lengths are 70 feet, about 63 feet, and about 94 feet.

THEATER DESIGN

Suppose your school is building a raked stage. The stage will be 30 feet long from front to back, with a total rise of 2 feet. A rake (angle of elevation) of 5o or less is generally preferred for the safety and comfort of the actors. Is the raked stage you are building within the range suggested?

ANSWER

The rake is about 3.8o, so it is within the suggested range of 5o or less.

Solve a right triangle that has a 40o angle and a 20 inch hypotenuse.

ANSWER

40o, 50o, and 90o, about 12.9 in., about 15.3 in. and 20 in.