M2 5.5: Inverse Trig Ratios

Lesson 5.5: Inverse Trig Ratios

NC Math II Honors - Coleman
Unit 5: Relationships in Right Triangles

I can solve for missing angles in right triangles by applying inverse trigonometric ratios.

Learning Target:

Warm-Up

A few review problems to get our brains in trig mode!

Drag and Drop

sinA = ​

Placeholder

, cosA = ​

Placeholder

, tanA = ​

Placeholder

Drag these tiles and drop them in the correct blank above

Math Response

Type answer here

Correct Answer: 17.8

Deg^°

Rad

Math Response

Type answer here

Correct Answer: 38.1

Deg^°

Rad

Math Response

Type answer here

Correct Answer: 13.5

Deg^°

Rad

​We've been writing and solving equations using the trig ratios (sine, cosine, tangent) to determine missing side lengths of right triangles.

It turns out if you know the sin, cosine, or tangent ratio of an angle, you can use the inverse of the ratio (sin^-1, cos^-1, tan^-1) to find the measure of the angle.

​

In other words, if we know two sides we can determine the measures of the acute angles of the right triangle.​

Let's walk through one

​We're trying to find the value of x. (Typically the Greek letter theta Θ is used as the variable to stand for an angle measure).

​

From x the side labeled "15" is the opposite and the side labeled "24"​ is the hypotenuse.

​Back in the day we'd do 15 /24, get 0.625, then try to find that on a trig table.

​

(Somewhere between 38°​ and 39°, right?)

Modern-day equivalent:

Use the inverse sine function on a calculator

​Remember: Check to make sure your calc is in DEGREE MODE!

Multiple Choice

Set up an equation that could be used to solve for the variable.

Multiple Choice

Choose the correct ratio.

• sin^-1(9/20)

• cos^-1(9/20)

• tan^-1(9/20)

• cos^-1(20/9)

Multiple Choice

Find the measure of angle A.

• 24

• 90

• 66

• 42

Multiple Choice

• $$71.3$$  

• $$18.7$$  

• $$17.8$$  

• $$72.2$$  

Multiple Choice

Use inverse trig ratios to solve for the missing angle

• 32°
• 44°
• 61°
• 50°

Concept Check!

Let's see how you do with this and other related skills!

Multiple Choice

Solve for x. Round to the nearest tenth.

• 74.9
• 3.6
• 63.5
• 54.1

Multiple Choice

Find the measure of the missing angle.

• 49^o
• 50^o
• 41^o
• 33^o

Multiple Choice

Find the measure of the missing angle.

• 64^o
• 26^o
• 61^o
• 8^o

Multiple Choice

What is the length of side x?

• 6.57 cm
• 7 cm
• 7.44 cm
• 26.33 cm

Multiple Choice

Solve the right triangle.

• <B = 39^o, AB = 11.58, AC = 7.29
• <B = 39^o, AB = 7.29, AC = 11.58
• <B = 129^o, AB = 11.58, AC = 7.29
• <B = 129^o, AB = 7.29, AC = 11.58

Multiple Choice

Solve the right triangle.

• <A = 33.7^o, <C = 56.3^o, AC = 5.59

• <A = 56.3^o, <C = 33.7^o, AC = 5.59

• <A = 33.7^o, <C = 56.3^o, AC = 9.01

• <A = 56.3^o, <C = 33.7^o, AC = 9.01

Poll

How well would you say you're doing with this learning target?

I can solve for missing angles in right triangles by applying inverse trigonometric ratios.

• I still need a lot of help to understand this.

• I'm getting there but I'll probably need some guidance.

• I'm getting it, some more practice and I'll have it down!

• I've totally got this. I can help peers if they need it!