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?

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Answer 1 · 2018-07-03T20:50:23

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

$A = (0,0)$

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

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

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

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

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

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

$x^2 + bx - 15525 = 0$

$b = -126,78547852 cdots$

$Delta = 78174,5575641cdots$

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

$x_1 = 203,1913cdots$

$x_2 = -76,4058279cdots$