Geometry Unit 8 Note Sheets 2016-1 - Geometry with …geometryhenry.weebly.com/uploads/5/6/5/5/56558273/...Geometry Unit 8 Note Sheets 7 Exploring Special Right Triangles (30-60-90)

Geometry Unit 8 Note Sheets

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Date Name of Lesson

The Pythagorean Theorem and its Converse

Exploring Special Right Triangles (45-45-90) Used with Special Rt Tri Pt 1

Special Right Triangles Part 1

Review for 45-45-90 Triangles

Exploring Special Right Triangles (30-60-90) Used with Special Rt Tri Pt 2

Special Right Triangles Part 2

Review for 30-60-90 Triangles

Worksheet Review of Special Right Triangles

Unit 8 Quiz 1

Trigonometry Part 1

Trigonometry Part 2

Trig Review or Activity

Unit 8 Quiz 2

Angles of Elevation and Depression

Clinometer Angles of Elevation and Depression Activity

Practice Test

Unit 8 Test


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The Pythagorean Theorem and Its Converse Notes Sheet Pythagorean Theorem Guided Practice Find x. 1. 2. Your Turn 3. 4. Pythagorean Triples


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Guided Practice Use a Pythagorean Triple to find x. Explain your reasoning. 5. 6. Your Turn 7. 8. Converse of the Pythagorean Theorem Pythagorean Inequality to Prove Acute Triangles Pythagorean Inequality to Prove Obtuse Triangles Guided Practice Determine whether each set of numbers can be the measures of a triangle. If to, classify the triangle as acute, right or obtuse. Justify your answer. 9. 7, 14, 16 10. 6.2, 13.8, 20 Your Turn 11. 9, 12, 15 12. 10, 11, 13


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Exploring Special Right Triangles (45-45-90) Given the isosceles right triangle to the right… 1. What is the measure of each angle? Explain 2a. If the length of each leg is 1 unit, find the length of the hypotenuse. Leave your answer in simplified rational form. 2b. What are the side-length ratios of leg : leg : hypotenuse? 3. If the length of each leg is 2 unit, find the length of the hypotenuse. Leave your answer in simplified rational form.


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Special Right Triangles Part 1 Notes Sheet 45° − 45° − 90° Triangle Theorem Guided Practice Find x. 1. 2. Your Turn 3. 4. Guided Practice 5. 6.


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Your Turn 7. 8. Guided Practice Find x and y. 9. Your Turn 10.


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Exploring Special Right Triangles (30-60-90) Given the equilateral triangle to the right whose sides are 2 units long… 1. What is the measure of each acute angle? 2. Fold the triangle along vertex A so that vertex B maps onto vertex C. Draw a segment along the crease. Label point D where the new segment intersects BC. What is special about AD? What is the length of BD (label it in the diagram)? Explain your reasoning. 3. What does AD do to angle A? 4. Examine triangle ABD. What is the measure of angle BAD and BDA (Label it in the diagram above)? 5. Find the length of AD. Leave your answer in simplified radical notation.


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Special Right Triangles Part 2 Notes Sheet 30° − 60° − 90° Triangle Theorem Guided Practice Find x and y. 1. 2. 3.


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Your Turn 4. 5. Guided Practice Your Turn Find x and y. 7. 6. Guided Practice 6.


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Trigonometry Part 1 Notes Sheet Words Symbols

Sine

Cosine

Tangent

Guided Practice Express each ratio as a fraction and as a decimal to the nearest hundredth. 1. 𝐬𝐢𝐧𝑷 2. 𝐬𝐢𝐧𝑸 3. 𝐜𝐨𝐬𝑷 4. 𝐜𝐨𝐬𝑸 5. 𝐭𝐚𝐧𝑷 6. 𝐭𝐚𝐧𝑸 Your Turn 7. 𝐬𝐢𝐧𝑲 8. 𝐜𝐨𝐬𝑲 9. 𝐭𝐚𝐧𝑲 10. 𝐬𝐢𝐧 𝑱 11. 𝐜𝐨𝐬 𝑱 12. 𝐭𝐚𝐧 𝑱


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Guided Practice Find x to the nearest hundredth. 13. 14. Your Turn 15. 16. Guided Practice 17. Use a special right triangle to express the tangent of 30° as a fraction and as a decimal to the nearest hundredth. Your Turn 18. Use a special right triangle to express the cosine of 45° as a fraction and as a decimal to the nearest hundredth. Guided Practice 17. A certain part of a hiking trail slopes upward at about a 5° angle. After traveling a horizontal distance of 100 feet along this part of the trial, what would be the change in the hiker’s vertical position? What distance has the hiker traveled along the path? Your Turn 18. A fitness trainer sets the incline on a treadmill to 7°. The walking surface is 5 feet long. Approximately how many inches did the trainer raise the end of the treadmill from the floor?


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Trigonometry Part 2 Notes Sheet Inverse Trigonometric Ratios

Inverse Sine Inverse Cosine Inverse Tangent Guided Practice Use a calculator to find the measure of ∠𝐴 to the nearest tenth. 1. 2. Your Turn 3. 4. Guided Practice


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5. Solve the right triangle. Round side measures to the nearest tenth and angle measures to the nearest degree. 𝑚∠𝑋 𝑚∠𝑌 𝑋𝑌 Your Turn Solve the right triangle. Round side measures to the nearest tenth and angle measures to the nearest degree. 6. 7.


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Angles of Elevation and Depression Notes Sheet Vocabulary: Angle of elevation __________________________________________________________________________

__________________________________________________________________________________________

Angle of depression _________________________________________________________________________

__________________________________________________________________________________________

Guided Practice Name the angle of depression or angle of elevation in each figure. 1. 2. Your Turn 3. 4. Guided Practice 5. Jay is meeting friends at the castle in the center of an amusement park. He sights the top of the castle at an angle of elevation of 38°. From the park’s brochure, she knows that the castle is 190 feet tall. If Jay is 5.5 feet tall, about how far is he from the castle to the nearest foot? Your Turn 6. The cross bar of a goalpost is 10 feet tall. If a field goal attempt is made 25 yards from the base of the goalpost that clears the goal by 1 foot, what is the smallest angle of elevation at which the ball could have been kicked to the nearest degree? (hint is everything in the same units of measure?)


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Guided Practice 7. A search and rescue team is airlifting people from the scene of a boating accident when they observe another person in need of help. If the angle of depression to this other person is 42° and the helicopter is 18 feet above the water, what is the horizontal distance from the rescuer to this person to the nearest foot? Your Turn 8. A lifeguard is watching a beach from a line of sight of 6 feet above the ground. She sees a swimmer at an angle of depression of 8°. How far from the tower is the swimmer? Guided Practice 9. Mia is at the top of a cliff and sees a seal in the water. If the cliff is 40 feet above the water and the angle of depression is 52°, what is the horizontal distance from the seal to the cliff, to the nearest foot? Your Turn 10. A hockey player takes a shot at a distance of 20 feet away from a 5-foot goal. If the puck travels at a 15° angle of elevation towards the center of the goal, will the player score?


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Clinometer Angles of Elevation and Depression Activity Instructions What is a Clinometer? A Clinometer is a device used to measure an angle of elevation or depression.

How do I use a Clinometer? There are a few steps to follow:

1. Decide on an object you want to determine the height for. 2. Determine the distance you are standing from the object. 3. Hold up the Clinometer to eye and line up the object through the straw. 4. Have a partner read the angle measurement.

Now there are a few things to go over about this Clinometer. Remember this is a protractor, so you have to look at it and think about how the angles work:

Now this is a measure of 90° however, if you think of what you would be looking at this would be an angle of elevation of 0°. So let’s look at a different angle: Now this looks like70°. But you have to remember that

the last time it looked like 90°, and so we are going to have to convert this.


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Below is similar to what we have on the figure above that looked like 70°. Let’s fill in some pieces and determine what is the angle of elevation. So that means that the rule that we use to find the angle of elevation would be: ________________________ What do you think will happen for the angle of depression? _______________________________________ Now that you have your angle there is one more thing that you need to think about before you can start calculating the height. Look at the figure below and see if you can figure out what you need to think about.

Geometry Unit 8 Note Sheets 2016-1 - Geometry with …geometryhenry.weebly.com/uploads/5/6/5/5/56558273/...Geometry Unit 8 Note Sheets 7 Exploring Special Right Triangles (30-60-90)

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