# Algebra II

An airplane leaves airport A and flies 200 km. At this time its bearing from Airport B, 250 km to the west, is 120 degrees. How far is the airplane from B?

1. 👍
2. 👎
3. 👁
1. let the plane's position be P
so in triangle ABP, angle A = 30° ( a bearing of 120 = 90+30)
let's find angle P
sinP/250 = sin 30/200

(case 1)
angle P = 38.682
then angle A = 113.328°
BP/sin113.328 = 200/sin30
BP = 372.63 km

case 2
angle P = 141.318
then angle A = 8.682°
BP/sin8.682 = 200/sin30
BP = 60.38 km

both answers make sense, since the triangle results in the "ambiguous case"

1. 👍
2. 👎
2. 1. A passenger in an airplane at an altitude of 10 km sees two towns to the east of the plane. The angle of depression to town A is 28o and the angle of depression to town B is 55o. How far apart are the two towns?

1. 👍
2. 👎

## Similar Questions

1. ### Trigonometry

A plane leaves airport A and travels 560 miles to airport B at a bearing of N32E. The plane leaves airport B and travels to airport C 320 miles away at a bearing of S72E. Find the distance from airport A to airport C.

2. ### math

An airplane is 120 miles north and 85 miles east of an airport. Find the bearing from the airplane to the airport (round to 1 decimal place)?

3. ### Trigonometry

A plane is 160 miles north and 85 miles east of an airport. If the pilot wants to fly directly to the airport, what bearing would be taken?

4. ### math

An aeroplane flies due north from Ikeja Airport for 500km. It then flies on a bearing of 060 degrees for a further distance of 300km before overflying a road junction.Calculate a. The distance of the aeroplne from Ikeja Airport

1. ### Trig

A plane is 48 miles west and 49 miles north of an airport. The pilot wants to fly directly to the airport. What bearing should the pilot take? In degrees and minutes

2. ### Maths

An Aeroplane X Whose Average Speed Is 500km/h Leaves Kano Airport At 7:00am And Travels For 2 Hours On A Bearing 050 Degree. It Then Changes Course And Flies On A Bearing 120 Degree To An Airstrip A. Another Aeroplane Y Leaves

3. ### Maths2

A plane leaves an airport X,20.6degree east and 36.8 degree north,and flies due south along the same longitude for 8hrs at the rate of 1000km/h to another airport Y,20.6 degree east and tita degree south.the plane then flies west

4. ### Mathematics

An aeroplane leaves an airport A and flies on a bearing 035°for 1.5 hours at 600km/hr to airport B It then flies on a bearing 130° for 1.5hours at 400km per hour to an airport C calculate the distance from C to A and the bearing

1. ### Pre Cal

An airplane leaves an airport and flies due west 150 miles and then 230 miles in the direction S 39.67 degrees W. How far is the plane from the airport at this time to the nearest mile.

2. ### trig

Two Airplanes leave an airport at the same time on different runways. One flies on a bearing of N66degreesW at 325 miles per hour. The other airplane flies on a bearing öf S26degreesW at 300 miles per hour. How far apart will the

3. ### trig

A plane is flying at an elevation of 30000 feet. It is within sight of the airport and the pilot finds that the angle of depression to the airport is 18. Find the distance between the plane and the airport. Find the distance

4. ### math

An airport passes over an airport and continues flying on a heading of N 70¡ãW for 3 km. The airplane then turns left and flies another 2 km until the airport is exactly due east of its position. What is the distance between the