Assignment. Framing a Picture Similar and Congruent Polygons
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1 Assignment Assignment for Lesson.1 Name Date Framing a Picture Similar and Congruent Polygons Determine whether each pair of polygons is similar. If necessary, write the similarity statement. Determine whether each pair of polygons is congruent. If necessary, write the congruence statement. 1. A 2 ft F 1 ft E B 3 ft 6 ft 3.5 ft H 2 ft 7 ft G D ft C 2. L 3 m 5 m P 5 m m R M m N 3 m Q Chapter Assignments 87
2 3. Is EMA congruent or similar to OMP? E A M P O. Draw two congruent right triangles that share only one common side. Label the triangles and list all of their corresponding parts. Write a congruence statement for your triangles. 88 Chapter Assignments
3 Assignment Assignment for Lesson.2 Name Date Wheelchair Ramps The Tangent Ratio Use the following figure, which represents a ramp, to complete Questions 1 through 3. Ramp Length Run of Ramp Rise of Ramp 1. The rise of the ramp is 1.5 feet and the run of the ramp is 21 feet. Find the slope of the ramp. 2. The rise of the ramp is 8 inches and the run of the ramp is 8 feet. Find the slope of the ramp. 3. A slope of 1:10 is used to construct a ramp that has a run of 2.5 feet. Define a variable for the rise of the ramp and determine its value in feet. Chapter Assignments 89
4 Use the following figure, which represents a roof truss, to complete Questions through 6. B h A 32 D 20 ft C. Determine the height of the roof truss if triangle ABD is congruent to triangle CBD. Round your answer to the nearest hundredth. 5. Find the measure of ABD. Then find the tangent ratio for that angle. 6. Find the length of AB. 90 Chapter Assignments
5 Assignment Assignment for Lesson.3 Name Date Golf Club Design The Sine Ratio Use the following figure and the given information to answer Questions 1 and 2. The Occupational Safety and Health Administration is the part of the U.S. government that ensures the safety and health of U.S. citizens by creating and enforcing standards for workplace environments. Standard (f)(3) refers to mobile ladder stands and scaffolds and states that the slope of the steps section shall be a minimum of fifty-five (55) degrees and a maximum of sixty (60) degrees, measured from the horizontal. Note that this regulation refers to an individual step on a mobile ladder stand. B y Vertical Height of Step A x C Horizontal Distance of Step 1. Suppose that the length of the step (length of AB) is 12 inches and m A 55. Find the vertical height and horizontal distance of the step. Chapter Assignments 91
6 2. Suppose that the length of the step (length of AB) is 12 inches and m A 60. Find the vertical height and horizontal distance of the step. Use following figure, which represents a roof truss, to complete Questions 3 and. B 16 ft h 3 A D C 3. Determine the height of the roof truss. Round your answer to the nearest hundredth.. Find the measure of ABD. Use the sine of that angle to find AD. 92 Chapter Assignments
7 Assignment Assignment for Lesson. Name Date Attaching a Guy Wire The Cosine Ratio Use the following figure and the given information to answer Questions 1 through. Quadrilateral ABCD is a square measuring 1 centimeter on each side. Segment BD is a diagonal. A B D C 1. What kind of triangle is DBC? 2. What is the measure of CDB? Explain your reasoning. 3. Determine the exact length of the diagonal. (Leave your answer in radical form, rather than using your calculator to approximate the answer.). Note that the diagonal is also the hypotenuse of the triangle. Find the exact values of sin 5º, cos 5º, and tan 5º. Chapter Assignments 93
8 5. The perpendicular bisector, YW, in the following figure creates a 30º-60º-90º right triangle XYW. Y 30 2 meters 2 meters 60 X 1 meter W Z 2 meters a. Determine the exact length of the perpendicular bisector. b. Note that the perpendicular bisector is a leg of the 30º-60º-90º right triangle. Determine the exact values for the sine, cosine, and tangent of both a 30 angle and a 60 angle. sin 30º sin 60º cos 30º cos 60º tan 30º tan 60º 9 Chapter Assignments
9 Assignment Assignment for Lesson.5 Name Date Using a Clinometer Angles of Elevation and Depression Use the given information to complete Questions 1 and 2. With its radar, an aircraft spots another aircraft 8000 feet away at a 12 angle of depression. 1. Draw a diagram that models this situation. Label the angle of depression and the hypotenuse. Label the side adjacent to the angle of depression as x and the side opposite the angle of depression as y. 2. Determine the vertical distance and the horizontal distance between the two aircraft. Chapter Assignments 95
10 Use the given information to complete Questions 3 and. When a space shuttle returns from a mission, the angle of its descent to the ground from the final 10,000 feet above the ground is between 17 and 19 with the horizontal. 3. Draw a diagram that models this situation. Label the angle of depression and the side opposite the angle of depression. Label the side adjacent to the angle of depression as x and the hypotenuse as z.. Based on the fact that the angle of depression is between 17 and 19, determine the minimum and maximum horizontal distance between the landing site and where the descent begins. 96 Chapter Assignments
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Name: ate: 1. ship at sea heads directly toward a cliff on the shoreline. The accompanying diagram shows the top of the cliff,, sighted from two locations, and B, separated by distance S. If m = 30, m
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Page 1 of 22 hapter 7: Right Triangles and Trigonometr Name: Stud Guide lock: 1 2 3 4 5 6 7 8 SOL G.8 The student will solve real-world problems involving right triangles b using the Pthagorean Theorem