A ship is approaching a lighthouse the is known to be 30 meters in height. The apparent size of the lighthouse is. 005 radians. Ten minutes later, the lighthouse has an apparent size of. 1 radians. How fast is the ship traveling.

Refer to the diagram shown below.

Let the ship approach the lighthouse at a constant speed of v km/h.

When the angle of elevation is 0.005 radians,

tan (0.005) = 30 / (x + y)

x + y = 30/tan (0.005) = 6000 m (1)

When the angle of elevation is 0.1 radian,

tan (0.1) = 30/x

x = 30/tan (0.1) = 299 m

From (1), obtain

y = 6000 - 299 = 5701 m = 5.701 km

The ship travels 5701 m in 10 minutes. It's speed is

v = (5.701 km) / (1/6 h) = 34.2 km/h

Answer: The ship is traveling at 34.2 km/h.