Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Rational trigonometry wikipedia , lookup
Perceived visual angle wikipedia , lookup
Multilateration wikipedia , lookup
Integer triangle wikipedia , lookup
History of trigonometry wikipedia , lookup
Pythagorean theorem wikipedia , lookup
Trigonometric functions wikipedia , lookup
Name _________________________________________ Date ____________________ Problem Solving: Mixed Problem Solving For use with the lesson “Measure and Classify Angles”, “Describe Angle Pair Relationships”, and “Classify Polygons” 1. Multi-Step Problem The diagram shows four airport runways and their intersections. All runways are straight and MQ bisects NTR. Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. a. Which angles are acute? obtuse? right? b. If m SVR = 56°, m NTO = 44°, and m QUP = 19°, find m PVR, m OTQ, m MUS, m MTO, m LTM. 2. Open-Ended The square piece of paper below has been folded in half three times and labeled as shown. Name 3 acute angles, 5 right angles, and 3 congruent obtuse angles. 3. Gridded Answer The diagram shows a ramp that is placed between the ground and a truck bed to load a bicycle. Find m MKL in degrees. 4. Short Response The table shown below is shaped like a regular pentagon. Use the diagram to find the length of a side. Explain. 5. Gridded Answer Suppose that between sunrise and sunset, the sun travels across the sky in a perfect half circle. When the setting sun is just 24° above the western horizon, what is the angle formed by the sun and the eastern horizon, in degrees? 6. Short Response A roof truss for John’s house is designed using 6 pieces of wood that form 4 triangles. The three inner pieces are called the truss web. The left and right pieces of the truss web meet at a right angle. The middle piece of the truss web bisects the straight angle of the bottom chord and divides the quadrilateral formed into two congruent triangles. The two pieces that form the top chord meet at a 120º angle. a. What are the measures of angles A-F? b. If the sum of the measures of the angles of a triangle is 180° what are the measures of angles G-L? Answer Key Lesson 1.6 Problem Solving Workshop: Mixed Problem Solving 1. a. acute: ∠LTM, ∠NTO, ∠OTQ, ∠PUQ, ∠RVS, ∠RTL, ∠NVP, ∠MUS; obtuse: ∠LTN, ∠MTO, ∠OTR, ∠PUM, ∠QUS, ∠RVP, ∠SVN, ∠LTQ; right: ∠MTN, ∠NTQ, ∠QTR, ∠RTM b. m∠PVR = 124, m∠OTQ = 46, m∠MUS = 19, m∠MTO = 134, m∠LTM = 46 2. Answers will vary. 3. 150 4. 42 in.; 17.5 feet; Sample answer: In a regular pentagon, all sides have equal length. Because you know the expressions for the length of two sides, set the expressions equal to each other to find x. Then substitute this value into one of the expressions to find the length of a side. 5. 156 6. a. m∠A – D = 45, m∠E – F = 60 b. m∠G = 75, m∠H = 105, m∠I + J = 30, m∠K = 105, m∠L = 75