A plane flies in a direction of 85 degrees from Chicago. It then turns and flies in the direction of 200 degress for 150 miles. It is then 195 miles from its starting point. How far did the plane fly in the direction of 85 degrees?

Question

3379 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-07-03T20:50:23

#203# miles because negative is actually #85^0 + 180^0#

#A = (0,0)#

#B = (x * cos 85^0, x * sin 85^0)#

#C = B + (150 * cos 200^0, 150 * sin 200^0)#

#|AC| = 195 = sqrt{C_x^2 + C_y^2}#

#195^2 = (x * cos 85 + 150 * cos 200)^2 + (x * sin 85 + 150 * sin 200)^2#

#195^2 = (x^2 * cos^2 85 + 150^2 cos^2 200 + 300x * cos 85 * cos 200) + (x^2 * sin^2 85 + 150^2 sin^2 200 + 300x * sin 85 * sin 200) #

#195^2 = x^2 + 150^2 + x * (300 * cos 85 * cos 200 + 300 * sin 85 * sin 200) #

#x^2 + bx - 15525 = 0#

#b = -126,78547852 cdots#

#Delta = 78174,5575641cdots#

#x = (-b pm 279,59713439895cdots)/2#

#x_1 = 203,1913cdots#

#x_2 = -76,4058279cdots#