Question

two radar stations A and B are 80km apart and B is due east of A.One aircraft is on a bearing 030 from A and 346 fromB. A second aircraft is on a bearing of 325 from A and 293 from B.How far apart are the two aircraft?

Answer 1

Given:

please find the question.

To find:

distance=?

Solution:

point: $A(0,0) \ \ \ \ \ B(80, 0)$

Claculating Slop of AC, $\tan 60^{\circ} = \sqrt{3} = 1.732$  

Claculating Slop of BC, $\tan 104^{\circ} = - 4.011$

Claculating Slop of AD, $\tan 125^{\circ} = - 1.428$

Claculating Slop of BD, $\tan 157^{\circ} = - 0.424$

When point C intersepts:

$\to y= 1.732 x......(a)\\\to y= -4.011(x - 80)......(b)$

solve equartion (a) and (b):  

$\to x_1 = 55.873 \\\to y_1 = 96.772$

When point D intersepts:

$\to y= -1.428 x......(c)\\\to y= 0.424(x - 80)......(d)$

solve equartion (c) and (d):  

$\to x_1 = 18.315 \\ \to y_1 = -26.154$

Calculating diatance:

$\bold{D= \sqrt{(y_2-y_1)^2 +(x_2-x_1)^2}}$

by putting the value the distance is  "128.535" .