Answer to Question #168696 in Geometry for Gideon

Question #168696


Two men P and Q set off from a base camp R prospecting for oil. P moves 20km on a bearing of 250° and A moves 15km on a bearing of 60. Calculate the Distance of Q from P


2: bearing of Q from


1
Expert's answer
2021-03-07T17:02:44-0500

Let distance traveled man P is a, man Q is b and distance between P and Q is c. Angle between P-man way and Q-man way is "250^0-60^0=190^0" . So we have a triangle with two sides ("a" and "b") and an angle between them (1900), and a side "c" which we have to find. According law of cosines: c2=a2+b2- 2*a*b*cos(1900). So

"c=\\sqrt{a^{2}+b^{2}-2*a*b*cos(190^0)}"

"c=\\sqrt{20^{2}+15^{2}-2*20*15*cos(190^0)}"

"\u0441\\approx24.19 (km)" - distance of Q from P.


What I need to find in task #2 is not known.


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