Lesson T-3 Trig Applications Name:

Transcription

1 Lesson T-3 Trig Applications Name: W e now ave two powerful tools for working wit rigt triangles te Pytagorean teorem and trigonometry. Fortunately, situations involving rigt triangles are very common. Let s practice finding missing sides, to te nearest tent. Eample 1: A street ligt spreads out its ligt at an 80 angle. Wen te ligt is suspended on a pole above a sidewalk, 60 feet of sidewalk are illuminated. How ig up is te ligt? Solution: First, draw a sketc: Second, write an equation. Since we know only 1 ft ft side, we must use trigonometry rater tan te Pytagorean teorem. We know te side opposite te reference angle, and we need te side adjacent to it. We sould use te tangent ratio. tan 40 o Tird, solve te equation: Fourt, answer te original question in a sentence: Te ligt is about 35.8 ft above te sidewalk. 1. A 100 ft guy wire from an airport communication tower forms a 70 angle wit te ground. How tall is te tower? 100 ft Eample 2: A baseball diamond is a square 90 ft on eac side. How far is it across te diagonal, from ome plate to second base? Solution: First, draw a sketc: Second, write an equation. Since te angles are 90 ft rigt angles and we know 2 sides of eac triangle, we can use te Pytagorean teorem to find te tird d Tird, solve te equation: d d d d Fourt, answer te original question in a sentence: Te distance from ome plate to second base is about ft. 2. An off-road entusiast drove 15 miles from a igway, straigt out into te desert. He came back at a different angle. If te trip back to te igway was miles, ow far down te road from is starting point did e come out? mi d 2 15 mi 90 ft 70 a Algebra 1 OBJ: Introduce using trigonometry to find a missing side T-3.A OBJ: Review using te Pytagorean Teorem

2 3. A 15-ft ladder is leaning against a building. If te top of te ladder makes a 20 angle wit te building, ow ig up te building does te ladder reac? 4. A flood ligt wit a dispersion angle of 100 needs to illuminate te front of a building ft wide. How far from te wall sould te ligt be positioned? 15 ft 15 ft 15 ft 20 b d For problems 5-8, assume eac diagram represents a situation. Solve for te missing side represented by te variable. Give your answer to te nearest tent, wit units in r 11 km f mi 2 mi 12 m p z Scrambled answers: ~5.2, 6.0, ~10.8, ~12.6, ~14.1, ~19.1, ~26.0, ~94.0 Algebra 1 OBJ: Introduce using trigonometry to find a missing side T-3.B OBJ: Review using te Pytagorean Teorem

3 T Planes, Trains, and Automobiles e previous activities ave all included te diagrams for you. In tis activity, you will need to draw your own as part of te solving process. Follow tese steps as you solve eac problem: Step 1: Draw a diagram. Label te information given, use a variable for wat you need to find. Step 2: Use trigonometry to write an equation tat can be solved for te variable. Step 3: Solve te equation. Step 4: Write te answer in a complete sentence. (Find sides to te nearest tent, and angles to te nearest degree.) Eample: After takeoff, a plane s fligt pat sends it directly over a town 3 miles from te airport. If it climbs at an angle of 10, ow ig above te ground will te airplane be wen it flies over te town (in feet)? Diagram: (Let = te plane s eigt in feet) Equation: tan 10 15,840 Solve: Since tan , we get ,840 Multiplying bot sides by 15,840 we get Answer: Te plane will be about 2,792.6 feet above te ground wen it flies over te town. Use te steps sown in te eample above as you solve eac word problem below. 1. A fireman, preparing to rescue a cild from a burning building, leaned a 35-foot ladder against te building at a 70 o angle (te angle between te ladder and te ground). How ig up te building did te ladder reac? 10 3 miles = = 15,840 ft 2. Bob and Rob were visiting te New York City. Tey observed tat wile standing 750 feet from Central Station, and looking up at a 23 o angle, tey could just see te top of te building. Using tis information, find te eigt of te Central Station building. Project Algebra 1 v7.1 OBJ: Epand using trigonometry to find a missing side T-3.C OBJ: Epand using trigonometry to find a missing angle

4 3. A driveway is constructed wit an 18% slope, almost te maimum allowed by te El Dorado County Transportation Department of 20%. Te angle of descent tat represents tis slope is 10 o. If te driveway surface is 1,260 feet long, ow many feet in elevation are lost from one end of te driveway to te oter? 4. Railroad engineers must be careful not to build a track too steep. A track needs to be built down a mountain tat drops 325 feet for every mile (5,280 ft) along te surface. At wat angle of descent sould te engineers build te track? 5. A pilot in an airplane is 4 miles from te airport were e intends to land (tis is straigt line distance from te plane to te runway). He is currently flying at an altitude of 10,000 feet. At wat angle sould te pilot descend in order to land on te runway? Scrambled answers: ~4 o, ~28 o, ~32.9, ~218.8, ~318.4 Project Algebra 1 v7.1 OBJ: Epand using trigonometry to find a missing side T-3.D OBJ: Epand using trigonometry to find a missing angle

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