Name _______________________________________________ Date _______ Lesson 2.20 – Finding Angles CC Geometry Do Now 1. Dan was walking through a forest when he came upon a sizable tree. Dan estimated he was about 40 meters

away from a tree when he measured the angle of elevation between the horizontal and the top of the tree to be 35 degrees. If Dan is about 2 meters tall, about how tall is the tree to the nearest meter?

Classwork

1. Dan was pretty impressed with this tree … until he turned around and saw a bigger one, also 40 meters away but in the other direction. “Wow,” he said. “I bet that tree is at least 50 meters tall!” Then he thought a moment. “Hmm … if it is 50 meters tall, I wonder what angle of elevation I would measure from my eye level to the top of the tree?” What angle will Dan find if the tree is 50 meters tall? Explain your reasoning.

In Algebra, we could solve 2 14x by doing the opposite of multiplying by 2, which is dividing. We also solved 2 9x by doing the opposite of squaring, which is taking the square root.

In trigonometry, to solve 1sin 2x we need to do the opposite of sin , which is arcsin .

1 sin 21arcsin(sin ) arcsin 21arcsin(sin ) arcsin 2

30

x

x

x

x

§ · ¨ ¸© ¹§ · ¨ ¸© ¹

2. Find the measure of angles a–c to the nearest degree.

a. b. c.

To solve in your calculator:

o check that your mode is in DEGREES

o turn the equation into

o which is the same thing as

o press and your calculator will display

o type in as using the division key

o hit enter to see the angle measure that has a sine value of

3. Shelves are being built in a classroom to hold textbooks and other supplies. The shelves will extend 10 in from the wall. Support braces will need to be installed to secure the shelves. The braces will be attached to the end of the shelf and secured 6 in below the shelf on the wall. What angle measure will the brace and the shelf make to the nearest degree?

4. A 16 ft ladder leans against a wall. The foot of the ladder is 7 ft from the wall. Determine the measure of

the angle formed by the ladder and the ground to the nearest degree.

5. A roller coaster travels 80 ft of track from the loading zone before reaching its peak. The horizontal

distance between the loading zone and the base of the peak is 50 ft. At what angle is the roller coaster rising to the nearest tenth of a degree?

6. For each triangle shown, use the given information to find the indicated angle to the nearest degree. a. b. c.

Homework 1. Given the following diagram:

(round to the nearest hundredth)

a) Find the measure of angle A b) Find the measure of angle B

2. Find the value of x and round your answers to the nearest tenth.

a) b) 3. Solve for x and round your answer to the nearest degree:

a) b) 4. Solve for x and round your answer to the nearest tenth:

a) b)

A

C B

7

18

xo

45 ft.

50 ft. 7 meters

50 meters

xo

A

C B

7

18