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Homework 3-solutions

Homework 3-solutions - kaplan(hmk378 Homework 3...

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kaplan (hmk378) – Homework 3 – Weathers – (17104) 1 This print-out should have 9 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 (part 1 of 2) 10.0 points Two sides of a triangle are 12 . 8 cm and 27 . 4 cm, with the included angle 115 . a) What is the length of the third side? Correct answer: 34 . 8 cm. Explanation: Basic Concepts: The Law of Cosines states c 2 = a 2 + b 2 - 2 ab cos C The Law of Sines states sin A a = sin C c Solution a c b A C We are looking for the side opposite the given angle so c = radicalbig a 2 + b 2 - 2 ab cos C 002 (part 2 of 2) 10.0 points b) What is angle opposite the side 12 . 8 cm? Correct answer: 19 . 4725 . Explanation: sin A a = sin C c A = arcsin parenleftbigg a sin C c parenrightbigg 003 10.0 points A high fountain of water is located at the center of a circular pool as in the figure. A student walks around the pool and estimates its circumference to be 180 m. Next, the student stands at the edge of the pool and uses a protractor to gauge the angle of elevation of the top of the fountain to be 73 . 8 . How high is the fountain? Correct answer: 98 . 6069 m. Explanation: R h θ The circumference of the pool is C = 2 πR so its radius is R = C 2 π = 180 m 2 π = 28 . 6479 m The radius and the height of the fountain form
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