Pre-AP Geometry Chapter 9 Test Review Standards/Goals: G.SRT.7./ H.1.b.: I can find the sine, cosine and tangent ratios of acute angles given the side lengths of right triangles. G.SRT.8/ H.1.c.: I can use trigonometric ratios to find the sides or angles of right triangles and to solve real-world problems o I can use angles of elevation and depression to find missing angles. G.SRT.10(+) I can use the law of sines and cosines to find missing side lengths or angle measures of a triangle. G.SRT.11.(+)/G.3.a.: I can use the law of sines or cosines to find the unknown measurements in a real-life situation. Extended standards (H.1.c.): o I can find the coordinates that describe a vector. o I can describe a vector using cardinal directions. o I can find the magnitude and direction of a vector. o Trigonometry Cotangent I can add vectors together. IMPORTANT VOCABULARY Trigonometric Ratios Angle of Elevation Sine Cosine Tangent Cosecant Secant Angle of Depression Law of Sines (AAS or SSA relationships) Law of Cosines (SAS or SSS relationships) Resultant Direction Compass/Cardinal Directions Right Triangle Trig: Find the missing parts. #1. Find n. #2. Find k. Vector 1 Magnitude #3. Find w. #4. Find x.
Vectors Use the vectors 3, 2, 1, 5, and 3, 5 to find each value. #5. Find the resultant and magnitude of and. 2 #6. Find the resultant and magnitude of and. #7. Consider the vectors <6, -5> and <-1, 5>. What would the magnitude be? #8. A helicopter takes off from its home base and travels 33 miles east and then 20 mi north. The result of the trip can be described by the vector 33,20. What are the magnitude and the direction of the flight vector? Round to the nearest tenth.
3 Law of Sines and Cosines #9. Find y in ΔXYZ if m<y = 38, <X = 50 and x = 14. Round to the nearest hundredth. #10. In ΔABC, a = 14, b = 9, and m<a = 44. Find m<b to the nearest degree. #11. Find the perimeter of the triangle:
4 Word Problems (Angle of elevation & depression) #12. A plane flying at an altitude of 8,000 feet begins descending when the end of the runway is below a point 30,000 feet away. Find the angle of descent (depression) to the nearest tenth of a degree. #13. A ship s sonar finds that the angle of depression to a wreck on the bottom of the ocean is 19.5 degrees. If a point on the ocean floor is 80 meters directly below the ship, how many meters, to the nearest METER, is it from that point on the ocean floor to the wreck? #14. A tree is broken during a violent thunderstorm. The top of the tree touches the ground at a point 31.2 feet from the foot of the tree and makes and angle of 29.3 degrees with the ground. Find the original height of the tree to the nearest tenth.
#15. A person whose eyes are 5.5 feet above the ground is standing on the runway of an airport 80 feet from the control tower. That person observes an air traffic controller at the window of the 102 foot tower. What is the angle of elevation to the nearest whole number? 5 #16. An observer at the top of a 68 foot tall lighthouse sights two ships approaching, one behind the other. The angles of depression of the ships are 31 degrees and 18 degrees. Find the distance BETWEEN the ships to the nearest foot (nearest integer). #17. An extension ladder is leaning against a wall at an angle of elevation of 47 degrees and the top of the ladder hits the wall 8.6 feet up. The ladder is then adjusted and moved higher and has an angle of elevation at this time of 59 degrees. Since the angle of elevation has changed, how much higher, TO THE NEAREST FOOT is the ladder than it originally was?
Additional Problems: #18. Determine the angle of elevation for the hill shown. 6 #19. Consider ΔDEF. If sin D = 0.4 and cos E = 0.123, what type of triangle is this? Consider the following: #20. Write sin 73ᵒ in terms of cosine. #21. Write cos 37ᵒ in terms of sine. #22. Compare sin 19 and cos 51. Which is the greater value? #23. A right triangle has an angle that measure 27 degrees and the adjacent side measures 19 feet. What is the length of the hypotenuse to the nearest hundredth? #24. Find x.
#25. Find w and x. 7 #26. A triangle has side lengths of 14, 17 and 28 units, respectively. Classify the triangle by its sides and angles. #27. Suppose that: <FGD = 90 degrees m<cge = 90 degrees m<bga = 138 degrees <EGH = <DGH. Consider the triangle shown: #28. What is the ratio of the sin Z? #29. What is the ratio of the tan X? #30. What is the ratio of the cos of Z?
8 Consider the triangle shown: #31. If WZ = 7 and ZY = 10, find WY in simplest radical form. #32. Draw an altitude from point Z and name all three altitudes in the triangle. #33. Find the length of the altitude that originates from point Z. #34. What is the sum of the lengths of all THREE altitudes. RELEVANT PORTIONS OF FORMULA SHEET FOR THIS TEST: