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?

1 Answer
Jul 3, 2018

203203 miles because negative is actually 85^0 + 180^0850+1800

Explanation:

A = (0,0)A=(0,0)

B = (x * cos 85^0, x * sin 85^0)B=(xcos850,xsin850)

C = B + (150 * cos 200^0, 150 * sin 200^0)C=B+(150cos2000,150sin2000)

|AC| = 195 = sqrt{C_x^2 + C_y^2}|AC|=195=C2x+C2y

195^2 = (x * cos 85 + 150 * cos 200)^2 + (x * sin 85 + 150 * sin 200)^21952=(xcos85+150cos200)2+(xsin85+150sin200)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) 1952=(x2cos285+1502cos2200+300xcos85cos200)+(x2sin285+1502sin2200+300xsin85sin200)

195^2 = x^2 + 150^2 + x * (300 * cos 85 * cos 200 + 300 * sin 85 * sin 200) 1952=x2+1502+x(300cos85cos200+300sin85sin200)

x^2 + bx - 15525 = 0x2+bx15525=0

b = -126,78547852 cdotsb=126,78547852

Delta = 78174,5575641cdots

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

x_1 = 203,1913cdots

x_2 = -76,4058279cdots