Name: ______Block: ______

Date: ______

Chapter 7

Right Triangles

and

Trigonometry

Sections Covered:

7.1-7.2 The Pythagorean Theorem & its Converse

7.3 Use Similar Right Triangles

7.4 Special Right Triangles

7.5-7.6 Trigonometry

7.7 Solve Right Triangles

The student will solve real-world problems involving right triangles by using the Pythagorean Theorem and its converse, properties of special right triangles, and right triangle trigonometry.

December / ~ January 2015 ~ / February ► /
Sun / Mon / Tue / Wed / Thu / Fri / Sat /
18 / 19 MLK DAY
/ 20 B / 21 A / 22 B
7.1-7.2 Pythagorean Thm & Converse
HW 7.1-7.2 Pythagorean Thm / 23 A
/ 24
25 / 26 Teacher Work Day / 27 A
7.3 Similar Right Triangles
HW: 7.3 and Review / 28 B
/ 29 A
7.4 Special Right Triangles
HW: 7.4 Special Right Triangles / 30 B
/ 31
◄ January / ~ February 2015 ~ / March ►
1 / 2 A
Review 7.1-7.4
HW: Quiz Review / 3 B
/ 4 A
***Quiz 7.1-7.4***
HW: Khan Academy / 5 B
/ 6 A
7.5-7.6 Trigonometry
HW: 7.5-7.6 Trig / 7
8 / 9 B
7.5-7.6 Trigonometry
HW: 7.5-7.6 Trig / 10 A
7.5-7.6 Trigonometry
HW: Trig Worksheet / 11 B
/ 12 A
7.7 Solving Right Triangles
HW: 7.7 Solving Right Triangles / 13 B
/ 14
15 / 16
Presidents Day / 17 A
Chapter 7 Test Review
HW: Review Worksheets / 18 B
/ 19 A
***Chapter 7 Test***
HW: Khan Academy / 20 B
/ 21

***Syllabus subject to change due to weather, pep rallies, illness, etc

Need Help?

Your teacher is available mornings and afternoons. Email them to set up a time!

Mu Alpha Theta is Monday, Tuesday, Thursday, and Friday mornings in L403.

Need to make up a test/quiz?

Math Make Up Room is open Tuesday, Thursday, and Friday mornings and Monday, Wednesday, and Thursday afternoons.

______

History: One of the most famous theorems in mathematics is the Pythagorean Theorem, named for the ancient Greek Mathematician Pythagoras (around 500 B.C.). This theorem can be used ______.

Theorem:

Ex1: Practice with the Pythagorean Theorem: Identify the unknown side as a leg or hypotenuse. Then, find the unknown side length of the right triangle. Write your answer in simplest radical form.

1. 2.

Pythagorean Triples: ______

4 Common Triples: Remember: All multiples are also triples.

EX4: Find the length of the third side using two methods.

Common Errors Using Triples: In a right triangle, if the two legs have lengths of 3 and 5, will the hypotenuse have a length four? Why or why not?

EX5: The lengths given are two sides of a right triangle. All three side lengths of the triangle are integers and together form a Pythagorean Triple. Find the length of the third side and tell whether it is a leg or a hypotenuse.

a. 28 and 45 b. 56 and 65

______

Pythagorean Theorem Converse: ______

______

Ex1: Tell whether a triangle with the given side lengths is a right triangle.

A. 15, 36, 39 B.

On Your Own:

1. 2. 10, 11, 14

Methods for Classifying a Triangle by Angles Using its Side Lengths:

Ex2: Determine whether the numbers can represent the side lengths of a triangle. If they can, classify the triangle as acute, right, or obtuse.

A. 8, 9, 10 B. 9, 7, 5

On Your Own:

1. 10, 12, 30 2. 16, 36, 30

Putting it all Together: Use two different methods to determine whether ∆ABC is a right triangle.

______

Theorem: If the ______is drawn to the ______of a

A. Let’s look at them separately.

B. State the altitude. ______

C. Now, let’s draw them so their corresponding parts have the same orientation.

D. Write a similarity statement.

Theorem 7.6 Geometric Mean (Altitude) Theorem 7.6 Geometric Mean (Leg)

Theorem Theorem

When both triangles share a common side, that side length is called the ______because this length is the positive value x that fits the proportion ______.

When you see this type of picture that has 3 similar right triangles always try Pythagorean Thm. first.

Ex2: Identify the similar triangles. Then solve for x. Round to the nearest tenth.

Small Triangle / Medium Triangle / Big Triangle
Small Leg
Medium Leg
Hypotenuse

Practice with Similar Right Triangles: Find the missing variable in simplest radical form. If possible, state the amount that represents the geometric mean.

Ex3: Ex4:

Small Triangle / Medium Triangle / Big Triangle
Small Leg
Medium Leg
Hypotenuse
Small Triangle / Medium Triangle / Big Triangle
Small Leg
Medium Leg
Hypotenuse

Practice: Find the value of the variable. Put answers in simplest radical form.

1.) 2.) 3.)

4.) 5.) 6.)

Ex1: Find the value of y. Write your answer in simplest radical form.

Ex2: Use any method to find all of the missing variables. (Use exact numbers.)

Word Problems:

Example 1: The diagram below shows a cross-section of a swimming pool. What is the maximum depth of the pool?

Find the altitude:

Tell whether the triangle is a right triangle. If so, find the length of the altitude to the hypotenuse. Round decimal answers to the nearest tenth.

1. 2. 3.

______

45°- 45°- 90° Triangle Theorem: In a 45°- 45°- 90° triangle, ______

______.

Hypotenuse = ______

Practice the 45°- 45°- 90° Pattern: Find the length of each missing side in simplest radical form.

Ex1: Ex2: Ex3:

On Your Own: Find the value of each variable in simplest radical form.

1. 2.

3. 4.

5. The body of a dump truck is raised to empty a load of sand. How high is the 14 foot body raised from the frame when it is tipped upward at a 45° angle?

30°- 60°- 90° Triangle Theorem: In a 30°- 60°- 90° triangle, ______

______and ______.

Hypotenuse = ______

Long Leg = ______

Practice the 30°- 60°- 90° Pattern: Find the length of each missing side in simplest radical form.

Ex1: Ex2: Ex3:

On Your Own: Find the value of each variable in simplest radical form.

1. 2.

3. 4.

5. The logo on the recycling bin at the right resembles an equilateral triangle

with side lengths of 6 centimeters. What is the approximate height of the logo?

All Mixed Up: Find the value of each variable. Write your answers in simplest radical form.

1. 2. 3.

4. 5. 6.

Classify: The side lengths of a triangle are given. Determine whether it is a 45° - 45° - 90° triangle, a 30° - 60° - 90° triangle, or neither.

1. 2. 3.

Complete the table.

1. 2.


______

Identifying Parts of Right Triangles: State the following, based on the diagram:

Name the hypotenuse: ______

Name the side opposite A: ______

Name the side adjacent theA and is not the hypotenuse: ______

Name the hypotenuse: ______

Name the side opposite B: ______

Name the side adjacent theB and is not the hypotenuse: ______

Find the length of the hypotenuse: ______Missing angle measures will use the variable______

Fact: We have been using formulas, proportions, and patterns all to find ______in right triangles. By using ______we are now able to find angles too. Trigonometry uses special ______to convert side lengths to angle measures. It’s really amazing! Because the conversion works all the time, each type of ratio has been given a special name; ______, ______, and ______!!!!

The acronym ______will help you to remember all of the ratios.

Ratios:

Ex1: State the Ratio: Find the following ratios:

1. sin B =

2. cos B =

3. tan B =

Ex2: Find a Missing Side Using Trig: Find the missing variable. Round to the nearest tenth.

1. 2.

On Your Own: Find the value of x. Round to the nearest tenth.

1. 2. 3.

x3: Multistep: Find the value of each variable to the nearest tenth.

*** Use exact numbers in your work and round at the very end. ***

Ex4: Area: Find the area of the triangle below to

the nearest tenth.

Ex6: Word Problems: Bobby is building a roof on a dog house. The front of the house is 4 feet long. The standard pitch/angle of elevation of a dog house roof is 35°. How long should he cut the support beam that runs from the side of the house diagonally up to the highest part of the roof to the nearest tenth?

Angle of elevation:

______

If you are asked to solve a right triangle, this means to:______.

In order to find the missing angles you will need to follow the following steps.

1.

2.

3.

To solve for an angle, undo each trigonometric operation by using their ______.

PRACTICE: Solve each equation to find the measure of angle A, to the nearest degree.

1. sin A = 0.5878 2. cos A = .1908 3. tan A =

Ex1: Use inverses to find the measure of angle A to the nearest degree.

a. b.

Ex2: Solve the right triangle in simplest radical form or to the nearest tenth.

1a. Missing side:

b. One of the missing angles:

c. The last missing angle:

2. Solve the right triangle in simplest radical form or to the nearest tenth.

On Your Own: Solve the right triangles in simplest radical form or to the nearest tenth.

1. 2.

Ex3: Applications in the Real World!!!!

If a 15 foot ladder is propped against the side of a garage and the base of the ladder is 8 feet from the side of the garage, what angle does the ladder make with the ground to the nearest degree?

Angle of Elevation

- always measured from the ground up

- always INSIDE the triangle

- movement of your eyes; you are looking straight

ahead and you must raise (elevate) your eyes to see

the top of a tree or building

Angle of Depression

- always OUTSIDE the triangle

- movement of your eyes; you are standing at the

top of a lighthouse and looking straight ahead, you

must lower (depress) your eyes to see the boat

Example 1: From a point on the ground

25 feet from the foot of a tree, the angle

of elevation of the top of the tree is 32˚.

Find, to the nearest foot, the height of

the tree.

3. You attend a music concert with some friends and sit halfway up the bleachers in the arena. The angle of depression from your horizontal line of sight to the stage is 24°. If your seat is 45 feet above stage level, what is your actual distance d from the stage? Round to the nearest foot.

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