Verified answer

ANGLE OF DEPRESSION

Problem:

The angle of depression from the top of the light house to two ships lying along the same line on the east of the light house at a given instant are 20 & 50 degrees respectively. If the top of the light house is measured at 30m above the sea level. What is the distance between the two ships at that instant?

Answer and Step-by-step explanation:

**See attached photo for illustration and detailed solution

In order to solve for the distance between two ships, we need to solve first the distance of each ship from the light house. Let us label the first ship as Ship A where the angle of depression from the top of the light house is 50 degrees and Ship B where the angle of depression from the top of the light house is 20 degrees.

As shown in the illustration, we can form triangles from which we can analyze the problem more clearly.

Applying the SOH-CAH-TOA, we have the opposite and the adjacent for each triangle where the opposite is 30 meters (which is the height of the light house), and x1 and x2 for the distance of Ship A and B from the light house respectively. The equation will be:

tanθ = opposite/adjacent

At Ship A:

tan50 = 30/x1

x1 = 30/tan50

x1 = 25.17 meters

So this is the distance from the lighthouse and Ship A.

At Ship B:

tan20 = 30/x2

x2 = 30/tan20

x2 = 82.42 meters

And this is the distance from the lighthouse and Ship B.

The distance between Ship A and B can be solved by subtracting x1 from x2. Hence:

x2 - x1 = 82.42 - 25.17

x2 - x1 = 57.25 meters

Therefore, the distance between the two ships at that instant is 57.25 meters.

Read more about angle of depression:

brainly.ph/question/2675078

#BRAINLYFAST