From the top of a lighthouse 210 feet high, the angle of depression to a boat is 27 degress. Find the distance from the boat to the food of the lighthouse. The lighthouse was built at sea level?
Please help and for some sugesstions
X tan27°=210'
Solve for X.
To solve this problem, we can use trigonometry and the concept of angles of depression.
Let's start by drawing a diagram:
B(boat)
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| /
| /
| /
|/ 27 degrees
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L(lighthouse)
The angle of depression is the angle formed between the line of sight from the top of the lighthouse to the boat and the horizontal ground.
Now, we need to find the distance from the boat to the foot of the lighthouse. Let's call this distance "x".
Using trigonometry, we can set up the tangent function:
Tan(27 degrees) = opposite/adjacent
In this case, the opposite side is the height of the lighthouse (210 feet) and the adjacent side is the distance from the boat to the foot of the lighthouse (x).
Therefore, the equation becomes:
Tan(27 degrees) = 210/x
To solve for x, we can rearrange the equation:
x = 210 / Tan(27 degrees)
Now, let's calculate the value of x:
x = 210 / Tan(27 degrees)
x ≈ 439.38 feet
So, the distance from the boat to the foot of the lighthouse is approximately 439.38 feet.
Suggestions:
- When working with trigonometry problems, it's important to visualize the situation and draw a diagram. This helps in understanding the given information and forming the appropriate trigonometric equation.
- Make sure you are using the correct trigonometric ratio for the problem at hand. In this case, we used the tangent function because we were given the angle of depression.
- Always double-check your calculations to ensure accuracy.