Find Distance Between Two Objects?

Question

A blimp, suspended in the air at a height of 500 feet, lies directly over the line from Soldier Field to the Adler Planetarium on Lake Michigan. If the angle of depression from the blimp to the stadium is 32 degrees and from the blimp to the planetarium is 23 degrees, find the distance BETWEEN Soldier Field and the Adler Planetarium.

Answer 1

Tan(x) = opp./adj.

tan(32) = s/500
500tan(32) = s

tan(23) = p/500
500tan(23) = p

p+s = distance between field and the planetarium

I don't have a calculator with me right now to get the tangent values. Just make sure your calculator is in degree mode (not radians).

Answer 2

tanθ = y / x

tan32 = 500 / x

xtan32 = 500

xtan32 / tan 32 = 500 / tan32

x = 500 / tan 32

x = 500 / 0.624869352

x = 800.1672645 feet

x = 800.2 feet

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tanθ = y/x

tan 23 = 500 / x

x tan 23 = x(500/x)

xtan23 = 500

xtan23 / tan23 = 500 / tan23

x = 500 / 0.424474816

x = 1177.926183 feet

x = 1178 feet rounded up

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The total distance

800.2 + 1178 = 1987.2 feet

The total distance is 1987.2 feet

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