gh07023
Answered

At Westonci.ca, we connect you with the answers you need, thanks to our active and informed community. Join our Q&A platform and connect with professionals ready to provide precise answers to your questions in various areas. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.

A fire is spotted from two lookout stations. The second station located ten miles due east of the first station. The bearing from the first station
to the fire is N 52° E. The bearing from the second station to the fire is N 37° W. To the nearest mile, find the distance from each lookout
station to the fire.

Sagot :

sqdancefan

Answer:

  • 8 mi from station 1
  • 6 mi from station 2

Step-by-step explanation:

From the first station, the angle between the direction of the other station (N90E) and the direction of the fire is 90-52 = 38°.

From the second station, the angle between the direction of the other station (N90W) and the direction of the fire is 90-37 = 53°.

We want to find the sides of the triangle with base angles 38° and 53° and base length 10 miles.  The a.pex angle will be 180°-38°-53° = 89°. The law of sines can be used.

  a/sin(A) = b/sin(B) = c/sin(C)

  a = sin(A)·c/sin(C) = sin(38°)·10/sin(89°) ≈ 6.16 ≈ 6 . . . miles (from sta 2)

  b = sin(B)·c/sin(C) ≈ sin(53°)·10.0015 ≈ 7.99 ≈ 8 . . . miles (from sta 1)

The fire is about 8 miles from the first station and 6 miles from the second station.

View image sqdancefan
We appreciate your visit. Hopefully, the answers you found were beneficial. Don't hesitate to come back for more information. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.