Answer to Question #164874 in Trigonometry for Jankarlos

Question

Two planes leave the Ottawa airport at the same time travelling at 920 km/h and 780 km/h. how far apart are the two planes after 3 hours, if the angle between their flight paths is 26°?

Answer 1

Let distance traveled by first plane is "a", distance traveled by second plane is "b" and distance between planes is "c". If angle between flights equal to 26⁰ using law of cosines: c²=a²+b²- 2*a*b*cos(26). So

$c=\sqrt{a^{2}+b^{2}-2*a*b*cos26}$

$a=920(km/h)*3(h)=2760 (km)$

$b=780(km/h)*3(h)=$ $2340 (km)$

$c=\sqrt{2760^2+2340^2-2*2760*2340*cos(26)}$ ,

$c\approx2176,48 (km)$