from the top of a tower, the angle of depression of a boat is 30degree,if the toweR is20meter high how far is th boat from the foot of the tower witha diagram
20 / d = tan(30º)
To calculate the distance of the boat from the foot of the tower, we can use trigonometry. Here's how you can do it:
1. Start by drawing a diagram representing the situation. Draw a vertical line to represent the tower and label it with its height, which is 20 meters. At the top of the tower, draw a horizontal line to represent the line of sight towards the boat.
2. Now, draw a line connecting the foot of the tower to the boat. This represents the distance we are trying to find. Label this line as "x" (as shown in the diagram).
3. Since we have the angle of depression, which is 30 degrees, we can label it on the diagram. The angle of depression is the angle between the horizontal line and the line connecting the top of the tower to the boat.
4. Now, looking at the right triangle formed by the tower, the line of sight, and the line connecting the top of the tower to the boat, we can use the trigonometric function tangent (tan) to calculate the distance x.
tan(angle) = opposite / adjacent
In this case, tan(30 degrees) = 20 / x
5. To solve for x, we need to isolate it.
x = 20 / tan(30 degrees)
6. Using a calculator, evaluate the expression on the right side of the equation:
x ≈ 34.64 meters
Therefore, the boat is approximately 34.64 meters away from the foot of the tower.
Note: The diagram is best understood when visualized, so it would be helpful to draw it out to better comprehend the solution process.