A ship is approaching a lighthouse known to be 30 meters height. The apparent size of the lighthouse is .005 radians. Ten minutes later, the lighthouse has an apparent size of 0.10 radians. How fast is the ship traveling in kilometers per hour?

Question

A ship is approaching a lighthouse known to be 30 meters height. The apparent size of the lighthouse is  .005 radians. Ten minutes later, the lighthouse has an apparent size of 0.10 radians. How fast is the ship traveling in kilometers per hour?

tylerd · Answer

wow this is a bit tricky, one sec

tylerd · Answer

ok

tylerd · Answer

since tan(theta)=opp/adjacent we can say

tan(0.005) = 30/x

where x is our distance away from the lighthouse.

to solve for x we get

x=30/tan(0.005)

tylerd · Answer

which comes out to about 6000 meters away from the lighthouse or about 6km

tylerd · Answer

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