Tamalpais Union High School District / Overview



Pre-CalculusName ________________________LAW OF SINES/COSINES – word problemsClasswork:1) A plane leaves Kittredgeville at a bearing of S24°E and flies at a speed of 400 mph for 2.5 hours. Over Norwood Town, the plane turns at a bearing of S80°E and continues for another 1.5 hours. a) Draw a picture of this situation.b) How far is the plane from the starting point?c) Through what angle would the pilot turn in order to head back to Kittredgeville?d) What is the bearing from the current location (after the 4 hours of flying back to Kittredgeville)?2) Ally is in the smaller building looking out of a window. She sights the top of the taller building at an angle of elevation of 40. She sights the bottom of the taller building with an angle of depression of 20. If the building is 200 feet tall, how high up is she in the smaller building? How far apart are the two buildings?17462539370003) A triangle has the given information: a = 2, b = 3, A = 20°.Find the area of the triangle. If two triangles are possible, find the area of both triangles.Mixed Trig! GROUPWORKSolve algebraically on [0, 2) in two different ways.4. 5. , a) b) 6. The Steamboat Natchez is one of the last steam-powered paddleboats in the US. It runs on the Mississippi in New Orleans. The wheel is 24 feet across and dips about 2 feet into the water to propel the boat through the river. Make a graph and write a sine function relating time to height (of a point on a blade) above the water.7. Solve for all solutions in radians.8. Find the exact value of: 9. Find the exact value of Pre-CalculusName ________________________LAW OF SINES/COSINES – word problems 1. Kris is taking a walk along a straight road heading East. He decides to leave the road, so he walks on a path with a bearing of N 55E. After walking for 450 meters, he turns right and heads back towards the road, ending up 676 meters from where he left the road. a) What angle did Kris turn to head back toward the road?b) How many meters did Kris walk?c) If Kris averaged 1.2meters/second how much time did he add to his walk by taking a detour on the path?2. Two radar stations are tracking the same plane. The angle of elevation from Station A to the plane is 67, the angle of elevation to the plane from Station B is 82. Station A is 3.2 miles from Station B. Find the distances from each station to the plane. What is the altitude of the plane?102997093345A00A3. Find the measure(s) of A in each triangle:7226308128030003013030205842024002473082710419800a) b) a = 20, b = 15, B=42 c) mC = 31, a = 16, c = 81036320137160400040 4. Find the area of the quadrilateral. 350520952512.6 cm0012.6 cm-10668015240015259051536708 cm008 cm1282700889046°0046° -2286001447807.2 cm007.2 cm5956305270542°0042°821690838208.6 cm008.6 cm5. Blake is taking a flight from Phoenix, AZ to San Francisco. There is a stopover in Las Vegas, NV. The bearing from Phoenix to Las Vegas is N42W. The bearing from Las Vegas to San Francisco is N71W. The distance of the first leg of the trip from Phoenix to Las Vegas is approximately 259 mi. From Las Vegas to San Francisco is another 413 mi. *All measurements here are approximate, but pretty close!* a) A direct flight from Phoenix to San Francisco without a stopover would be shorter; how much shorter?b) What is the bearing from Phoenix to SF?6. Two ships leave a harbor at the same time. One ship travels at a bearing of S12°W at 14 mph. The other ship travels on a bearing of N75°E at 10 mph. How far apart will the ships be after three hours? 7. Closed to tourists since 1990, the Leaning Tower of Pisa in Italy leans at an angle of about 84.7°. The figure shows that 171 feet from the base of the tower, the angle of elevation to the top is 50°. If a bird is sitting on the very top of the tower, how high is the bird?-1295404381587.7°171 ftbird0087.7°171 ftbird0-2540008. You are sailing a boat and need to get to an island that is 50 miles to the West of your current location. But there are rough seas along the direct route. To avoid this, you take a path at a bearing of 245 for 30 miles. How far away are you from the island and at what bearing must you now sail to get to the island? ................
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