Lesson 4.2.3 & 4.2.4

Lesson 4.2.3

Complete the first four questions labeled BELLWORK.

Multiple Select

BELLWORK: A fair six-sided dice is rolled and then a penny is flipped. Select which outcomes that are possible (in the sample space). (H=Heads, T=tails)

• 11

• 2T

• 3T

• 46

• 5H

Multiple Choice

BELLWORK: A fair six-sided dice is rolled and then a penny is flipped. What is the probability that the dice lands on a 4 and the coin lands on tails?

• 1/6

• 1/12

• 1/2

• 1/8

Multiple Choice

BELLWORK: A fair six-sided dice is rolled and then a penny is flipped. What is the probability that the dice lands on an even number?

• 1/6

• 1/12

• 1/3

• 1/2

Multiple Choice

BELLWORK: A fair six-sided dice is rolled and then a penny is flipped. What is the probability that the dice lands on an even number AND the coin lands on Heads?

• 1/4

• 1/2

• 1/12

• 1/6

Review Finding Missing Sides with Trigonometry

Work through the next 3 problems now, using what you learned last class. Write down any questions that you have as you answer each one. If you get it wrong, make sure you understand why. If you do not, that is a good question to ask: "For question _____ I did this. Why wasn't that correct?"

Multiple Choice

Find the missing value.

Round to the nearest tenths.

• 23.6 miles

• 4.6 miles

• .9 miles

• 20.7 miles

Multiple Choice

Find the missing value.

Round to the nearest tenths.

• 36.6 in

• 43.7 in

• 47.8 in

• 37.4 in

Multiple Choice

Find the missing value.

Round to the nearest tenths.

• 33.9 mm

• 3.4 mm

• 10.5 mm

• 36.2 mm

Inverse Trig Ratios & Applications

Today we will talk about how to find the missing angles of a right triangles using trigonometry, and how to draw triangles from word problems. Work through the next 4 questions to see what an inverse trig ratio is. STOP when you get to the next slide that is title "Inverse Operations".

Multiple Choice

If 60 $\degree$  is the REFERENCE angle of the triangle, how would you classify the side of length 8?

• opposite

• adjacent

• hypotenuse

Multiple Choice

If 60° is the REFERENCE angle of the triangle, how would you classify the side of length 16?

• opposite

• adjacent

• hypotenuse

Open Ended

What was so special about that answer, considering this triangle?

Inverse Operations

To determine angle measure from a trigonometric ratio (sine, cosine, tangent), you need to "undo" it, just like you can undo addition with subtraction, multiplication with division, or squaring by taking the square root. These are all examples of INVERSE OPERATIONS.

When you use a calculator to do this, you use inverse trigonometric functions that are usually labeled:

 $\sin^{-1}$  (called "inverse sine"),  $\cos^{-1}$  (called "inverse cosine"), and  $\tan^{-1}$  (called "inverse tangent").

Finding missing angles of right triangles

If you are at home, watch this video and take notes (write down everything he writes down). If you are in class, we will take go over this together.

Multiple Choice

Find the missing angle

• 15

• 37

• 66

• 72

Multiple Choice

What is the measure of angle x?

• 73.74 degrees

• 16.26 degrees

• 148 degrees

• 180 degrees

Multiple Choice

Find the measure of the angle. Round to the nearest tenth.

• 40.4

• 43.4

• 48.2

• 41.3

Multiple Choice

Find the measure of the angle. Round to the nearest tenth.

• 66.4

• 63.4

• 47.8

• 69.4

Multiple Choice

Find the measure of the indicated angle. Round to the nearest tenth.

• 48.9°

• 60.7°

• 29.3°

• 41.1°

Multiple Choice

Find the measure of the indicated angle. Round to the nearest tenth.

• 35.8°

• 43.8°

• 46.2°

• 54.2°

Multiple Choice

Find the measure of the indicated angle (?) round to the nearest tenth.

• 9.4

• 55.2

• 20.15

• 19.4

Multiple Choice

Which expression is correct for "y"?

• y = tan^–1(31/23)

• y = sin^–1(31/23)

• y = cos^–1(31/23)

Angle of ELEVATION and DEPRESSION

In word problems, the reference angles in right triangles can have special names.

Multiple Choice

Jeff forgot to put on his parking brake, so his car rolled off the side of a cliff. He is standing on the edge of the cliff looking down at his broken car at the bottom.

He knows the height of the cliff is 60 feet and it looks like his car is about 100 feet away from the base of the cliff. Which triangle represents this situation correctly?

Multiple Choice

If Jeff is looking down at his car, which angle represents the angle of DEPRESSION?

• Angle R

• Angle B

• The right angle

Multiple Choice

Angela is looking through binoculars at a bird in a tree. If the tree is 28 feet tall and she is standing 12 feet away from it, which triangle models the situation?

Multiple Choice

Is the angle that Angela looks up at the bird (angle B), an angle of ELEVATION or an angle of DEPRESSION?

• Angle of ELEVATION

• Angle of DEPRESSION

• Neither