The angle of depression from a water tower to a forest fire underneath the tower is 18°. If the height of the water tower is 60 meters, what is the horizontal distance on the ground between the water tower and the fire?
d = 60 cot 18° = 184.7m
To find the horizontal distance, we can use the tangent function.
First, let's define the variables:
θ = angle of depression = 18°
h = height of the water tower = 60 meters
Now, we can use the tangent function to find the horizontal distance (d):
tan(θ) = opposite / adjacent
In this case, the opposite side is the height of the water tower (h), and the adjacent side is the horizontal distance (d).
tan(18°) = h / d
Now, rearrange the equation to solve for d:
d = h / tan(18°)
Let's calculate the value of d using the given values:
d = 60 / tan(18°)
Using a scientific calculator, we find:
d ≈ 185.87 meters
Therefore, the horizontal distance between the water tower and the forest fire is approximately 185.87 meters.
To find the horizontal distance between the water tower and the fire, we can use trigonometry. In this scenario, we have the angle of depression (18°) and the height of the water tower (60 meters).
Let's assume that the horizontal distance we are looking for is represented by 'd'.
Now, we can use the tangent function, which relates the angle of depression to the opposite (height) and adjacent (horizontal distance) sides of a right triangle. The tangent of an angle is equal to the length of the opposite side divided by the length of the adjacent side.
Using the formula for tangent:
tan(18°) = height / horizontal distance
We can rearrange the equation to solve for the horizontal distance:
horizontal distance = height / tan(18°)
Plugging in the given values:
horizontal distance = 60 meters / tan(18°)
Now, let's calculate it:
horizontal distance ≈ 60 meters / tan(18°) ≈ 192.65 meters
Therefore, the horizontal distance between the water tower and the fire is approximately 192.65 meters.