AS OBSERVED FROM A 60M HIGH LIGHT HOUSE THE ANGLE OF DEPRESSION IS 30 AND 45 DEGREE.FIND THE DISTANCE BETWEEN THE SHIPS.
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tan 45 = 60/da
tan 30 = 60/db
To find the distance between the ships, we can use the concept of trigonometry and the angle of depression. Here's how you can get the answer:
Step 1: Draw a diagram
Start by drawing a diagram to represent the situation. Label the ship closest to the lighthouse as "A," the ship furthest from the lighthouse as "B," and the lighthouse as "L." Draw a line from point L vertically down to the sea to represent the height of the lighthouse.
Step 2: Identify the given information
In this problem, we have two angles of depression: 30 degrees and 45 degrees. We also know the height of the lighthouse, which is 60m.
Step 3: Use trigonometry to solve for the distance between the ships
Let's start with the ship at point A. With the 30-degree angle of depression, we can form a right triangle using the height of the lighthouse as the opposite side and the distance between the lighthouse and ship A as the adjacent side. Using the tangent function, we have:
tan(30) = opposite / adjacent
tan(30) = 60 / x
Simplifying, we get:
x = 60 / tan(30)
Similarly, for the ship at point B, we can use the 45-degree angle of depression to form another right triangle. Using the tangent function again, we have:
tan(45) = opposite / adjacent
tan(45) = 60 / y
Simplifying, we get:
y = 60 / tan(45)
Step 4: Calculate the distances
Now we can substitute the values of tan(30) and tan(45) using a scientific calculator to find the distances between the ships.
For ship A:
x = 60 / tan(30)
For ship B:
y = 60 / tan(45)
Evaluate the values on a calculator to get the final distances between the ships, given the height of the lighthouse is 60m.
Please note that the units for the distances will depend on the units you used for the height of the lighthouse.