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Contents Lesson 7-1Geometric Mean Lesson 7-2The Pythagorean Theorem and Its Converse Lesson 7-3Special Right Triangles Lesson 7-4Trigonometry Lesson 7-5Angles of Elevation and Depression Lesson 7-6The Law of Sines Lesson 7-7The Law of Cosines

Lesson 5 Contents Example 1Angle of Elevation Example 2Angle of Depression Example 3Indirect Measurement

Example 5-2a SHORT-RESPONSE TEST ITEM A wheelchair ramp is 3 meters long and inclines at Find the height of the ramp to the nearest tenth centimeter. Read the Test Item The angle of depression between the ramp and the horizontal is Use trigonometry to find the height of the ramp. Solve the Test Item Method 1 The ground and the horizontal level with the platform to which the ramp extends are parallel. Therefore, since they are alternate interior angles.

Example 5-2b Answer: The height of the ramp is about meters, Mulitply each side by 3. Simplify. YWYW

Example 5-2c Method 2 The horizontal line from the top of the platform to which the wheelchair ramp extends and the segment from the ground to the platform are perpendicular. So, and are complementary angles. Therefore, YWYW

Example 5-2d Answer: The height of the ramp is about meters, Multiply each side by 3. Simplify.

Example 5-2e SHORT-RESPONSE TEST ITEM A roller coaster car is at one of its highest points. It drops at a angle for 320 feet. How high was the roller coaster car to the nearest foot before it began its fall? Answer: The roller coaster car was about 285 feet above the ground.

Example 5-3a Vernon is on the top deck of a cruise ship and observes two dolphins following each other directly away from the ship in a straight line. Vernon’s position is 154 meters above sea level, and the angles of depression to the two dolphins are Find the distance between the two dolphins to the nearest meter.

Example 5-3b are right triangles. The distance between the dolphins is JK or Use the right triangles to find these two lengths. Because are horizontal lines, they are parallel. Thus, and because they are alternate interior angles. This means that

Example 5-3c Multiply each side by JL. Divide each side by tan Use a calculator.

Example 5-3d Multiply each side by KL. Use a calculator. Divide each side by tan Answer: The distance between the dolphins is, or about 8 meters.

Example 5-3e Madison looks out her second-floor window, which is 15 feet above the ground. She observes two parked cars. One car is parked along the curb directly in front of her window, and the other car is parked directly across the street from the first car. The angles of depression of Madison’s line of sight to the cars are Find the distance between the two cars. Answer: about 24 feet

End of Lesson 5

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