Answer Player two Explanation Given information: Soccer: A soccer player is standing 35 feet from one post of the goal and 40 feet from the other post. Another soccer player is standing 30 feet from one post of the same goal and 20 feet from the other post. Calculation: Draw the image. In this diagram player one is purple and player two is red. Use the law of cosines formula with the angle isolated to find the angles of each player. P 1 = cos − 1 35 2 + 40 2 − 24 2 2 ( 35 ) ( 40 ) Simplify and solve for the angle of player 1. P 1 = 36.56 ∘ Do the same for the player two. P 2 = cos − 1 20 2 + 30 2 − 24 2 2 ( 20 ) ( 30 ) Simplify and solve for the angle of player 2. P 2 = 66.28 ∘ Thus, player 2 has the greater angle, so the player 2 has the better shot.

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition

1st Edition

ISBN: 9780078682278

Author: McGraw-Hill, Berchie Holliday

Publisher: Glencoe/McGraw-Hill

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Question

Chapter 5.8, Problem 31E

To determine

Which player has a greater angle to make a shot on goal, if the goal is 24 feet wide?

Expert Solution & Answer

Answer to Problem 31E

Player two

Explanation of Solution

Given information: Soccer: A soccer player is standing 35 feet from one post of the goal and 40 feet from the other post. Another soccer player is standing 30 feet from one post of the same goal and 20 feet from the other post.

Calculation:

Draw the image. In this diagram player one is purple and player two is red.

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition, Chapter 5.8, Problem 31E

Use the law of cosines formula with the angle isolated to find the angles of each player.

P1=cos−1352+402−2422(35)(40)

Simplify and solve for the angle of player 1.

P1=36.56∘

Do the same for the player two.

P2=cos−1202+302−2422(20)(30)

Simplify and solve for the angle of player 2.

P2=66.28∘

Thus, player 2 has the greater angle, so the player 2 has the better shot.

Chapter 5.8, Problem 30E

Chapter 5.8, Problem 32E

Chapter 5 Solutions

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition

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