Peggy’s Cove Lighthouse, in Nova Scotia, is possibly the most photographed lighthouse in the world. From the observation deck, the angle of depression of a boat is 6º. How far is the boat from the lighthouse, to the nearest metre?
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To find the distance between the boat and the lighthouse, we can use trigonometry and the concept of angles of depression.
First, let's sketch the situation. We have the Peggy's Cove Lighthouse and a boat, with the observation deck being at a higher elevation. The angle of depression is the angle between the observer's line of sight and a line parallel to the horizontal plane.
Since we know the angle of depression, we can use the tangent function to calculate the distance between the boat and the lighthouse.
Tangent is defined as the ratio of the opposite side to the adjacent side of a right triangle. In this case, the opposite side is the vertical distance between the observation deck and the boat, and the adjacent side is the horizontal distance between the observation deck and the boat.
Let's assume the distance between the observation deck and the boat is 'x' meters.
Using the tangent function:
tan(angle of depression) = opposite/adjacent
tan(6º) = x/h
To find the adjacent side 'h' (distance between the boat and the lighthouse), we rearrange the formula:
h = x / tan(6º)
Now, we can substitute the given angle of depression into the equation and solve for 'h':
h = x / tan(6º)
Using a scientific calculator or trigonometric table, the tangent of 6º is approximately 0.1051.
Therefore, the formula simplifies to:
h = x / 0.1051
To find 'h', we need to know the value of 'x'. Unfortunately, the information provided in the question is insufficient to determine the value of 'x' or calculate the distance between the boat and the lighthouse accurately.
If you have access to the actual distance between the observation deck and the boat ('x'), you can substitute that value into the formula h = x / 0.1051 and calculate the distance ('h') in meters to the nearest meter.