BellworkSolve for x

x53

51

x13

12

x

1116

Clickers

Bellwork SolutionSolve for x

x53

51 . 53

. 38.45

. 41.19

A

B

C

Bellwork SolutionSolve for x

x13

12

. 62.53

. 13.29

. 2.72

A

B

C

Bellwork SolutionSolve for x

x

1116

. 5

. 3 15

. 377

A

B

C

Solve Right TrianglesSection 7.7

Chapter 7 Test on Wednesday (12/1)

The Concept Thus far we’ve primarily been focused on using the

sine, cosine and tangent functions when we already have the angles in which to use

Today we’re going to explore the inverse trig functions which allow us to calculate angle measures based on side lengths

Example

Typically, the inverse functions on a calculator are the Shift buttons above their respective trig functions

15sin

20 20

θ

15

Given the triangle below, find the sine of theta

In order to solve for theta, we know use the inverse sine

function1 15sin20

1sin .75

48.59

If using the back of the book, find the whole angle nearest the divided ratio being used

The Inverses

sinopp

hyp

Functionally, these inverse ratios are linked to their “regular” functions

adjcos

hyp

tanopp

adj

1sinopp

hyp

1cosadj

hyp

1tanopp

adj

In useSolve for θ

tan opp

adj

θ

21

21tan

37

37

1 21tan

37

29.578

On your ownWhat inverse trig ratio should be used in this situation?

5

4

. sin

. cos

. tan

A

B

C

On your ownWhat inverse trig ratio should be used in this situation?

53

. sin

. cos

. tan

A

B

C

On your ownWhat inverse trig ratio should be used in this situation?

4

3

. sin

. cos

. tan

A

B

C

On your ownWhat is the correct value for θ?

5

4

. 36.87

. 51.34

. 53.13

A

B

C

On your ownWhat is the correct value for θ?

4137

. 25.52

. 42.06

. 64.48

A

B

C

On your ownWhat is the correct value for θ?

16

12

. 48.59

. 53.13

. 86.42

A

B

C

On your ownWhat is the correct value for θ?

3 5

4

. 36.60

. 53.39

. 77.12

A

B

C

In useSolve for θ,Φ & x sin

opp

hyp

26

θ

21

21n

26si

x

Φ

1 21sin

26

53.87

2 2 226 21 x 2676 441 x

2235 x235 15.33x

180 90 90 53.87

36.13

15.33

53.87o

36.13o

On your ownWhat are the correct values for θ, Φ & x?

12

7

. 30.25,59.75,9.75

. 35.69,54.31,9.75

. 54.31,35.69,9.75

. 54.31,35.69,13.89

A

B

C

D

x

On your ownWhat is the correct values for θ, Φ & x?

15

9

. 36.87,53.13,12

. 53.13,36.87,12

. 53.13,36.87,17.49

. 54.31,35.69,17.49

A

B

C

D

x

Practical example

You are trying to build a ramp so that you can take your bike of some “sweet jumps.” The ramp will have a face of 12.5 feet and be 6.3 feet off the ground at the top. What is the angle of elevation for the ramp?

A. 30.26o

B. 38.44o

C. 59.74o

Homework

7.71, 2-40 even

Most Important Points• Inverse trig ratios• System for solving right triangles