Q. 37 Rescue at Sea Coast Guard Statio... [FREE SOLUTION]

91影视

Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 8: Q. 37 (page 528)

Rescue at Sea Coast Guard Station Able is located 150 miles due south of Station Baker. A ship at sea sends an SOS call that is received by each station. The call to Station Able indicates that the ship is located N55掳E; the call to Station Baker indicates that the ship is located S60掳E.
(a) How far is each station from the ship?
(b) If a helicopter capable of flying 200 miles per hour is dispatched from the station nearest the ship, how long will it take to reach the ship?

Short Answer

Expert verified

(a) The distance between Station Able and ship is is 143.33 miles and distance between ship and Station Baker is 135.58 miles.

(b) Time taken by the airplane is 0.678 hours or 40.67 minutes.

Step by step solution

Step 1. Given Information

Diagram according to the given information. A represent the position of Station Baker, Brepresent the position of Station Able while Crepresent the position of the ship.

Step 2. Finding angle C using angle sum property of a triangle

$鈭� C = 180 - (60 + 55) 鈭� C = 65^{慰}$

Part (a) Step 1. Finding distance between the Ship and Station Able

Apply Sin law and find length $a$

$\frac{a}{\sin (A)} = \frac{c}{\sin (C)} a = \sin (A) 脳 \frac{c}{\sin (C)} a = S i n 60^{慰} 脳 \frac{150}{\sin 65^{慰}} a = \frac{\sqrt{3}}{2} 脳 \frac{150}{0.906} a = 143.33$

Part (a) Step 2. Finding distance between Ship and Station Baker

$\frac{b}{\sin B} = \frac{c}{\sin C} b = \sin B 脳 \frac{c}{\sin C} b = \sin 55^{慰} 脳 \frac{150}{\sin 65^{慰}} b = 0.8191 脳 \frac{150}{0.9063} b = 135.58 k m$

Part(b) Step 1. Finding time to reach the ship by airplane

The distance between Ship and Station Baker is 135.57 miles. This is the shortest possible distance from a station to the ship. The speed of the helicopter is 200 miles per hour which means that the time taken for the helicopter to reach the ship is $\frac{135.57}{200} = 0.678 h o u r s$ .