Question

A ship is sighted at sea from the top of a light house 75 m high. If the angle of depression is found to
be 30° find the distance of ship from the light house (in meters).
​

Answer 1

Step-by-step explanation:

Let AB be the light house. The height (h) of the lighthouse from the sea level is AB = h = 75 m. Now the angle of depression of the ships is 30 degree and 45 degree and the one ship is exactly behind the other one on the same side of the light house

Answer 2

To Find:

• CD = distance between two ships

Solution:

Step 1: From right triangle ABC,

tan 45° = AB/BC

1= 75/BC

BC = 75 m

Step 2: Form right triangle ABD,

tan 30° = AB/BD

1/√3 = 75/BD

BD = 75√3

Step 3: To find measure of CD, use results obtained in step 1 and step 2.

CD = BD – BC = (75√3 – 75) = 75(√3-1)

The distance between the two ships is 75(√3-1) m

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