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Using Trigonometric Laws

Using Trigonometric Laws. Information. Fishing lake. This fishing lake needs to be stocked with fish for the season. Determine the width of the lake. Assume the lake is circular and of uniform depth 4.5 ft. Find the volume of the lake.

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Using Trigonometric Laws

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  1. Using Trigonometric Laws

  2. Information

  3. Fishing lake This fishing lake needs to be stocked with fish for the season. • Determine the width of the lake. • Assume the lake is circular and of uniform depth 4.5ft. Find the volume of the lake. • The lake should be stocked with one fish per 1000ft³ of water. How many fish should be put in the lake? • 15% of the fish should be left in the pond after fishing season closes. If there is a per person maximum catch of 20, what is the maximum number of fishing licenses that can be sold?

  4. Finding a length This fishing lake needs to be stocked with fish for the fishing season. a) Determine the width of the lake. The distance from the fisherman to one side of the lake is 486 ft. The distance to the other side is 408 ft. The angle between these distances is 78°. 408 ft 486 ft determine which law to use: 78° Law of Cosines a2 = b2 + c2 – 2bc cosA write the law: substitute for the given values: a2 = 4862 + 4082 – 2 ∙ 486 ∙ 408 ∙ cos(78°) a = evaluate: a = 566ft (to the nearest foot)

  5. Finding the volume • Assume the lake is circular and of uniform depth 4.5ft. Find the volume of the lake. identify which 3D object should be used to model the lake: The lake is assumed to be circular with uniform depth, so it can be modeled as a cylinder. determine the height and radius of the cylinder: height, h = 4.5ft 566 radius, r = = 283ft 2 write the formula for the volume, V, of a cylinder: V = πr2h substitute: V = π(2832)(4.5) evaluate: V = 1132232 cubic feet

  6. The solution • The lake should be stocked with one fish per 1000ft³ of water. How many fish should be put in the lake? 1132232 divide the volume by 1000: = 1132.232 1000 The lake should be stocked with 1132 fish before the fishing season. • 15% of the fish should be left in the lake after fishing season closes. If there is a per person maximum catch of 20, how many fishing licenses can be sold? For 15% of the fish to be left, a maximum of 85% can be caught. find 85% of 1132, to the nearest whole fish: 0.85 × 1132 = 962 fish 962 divide this number of fish by the maximum catch: = 48.1 20 Therefore, no more than 48 licenses should be sold.

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