a forest ranger spots a fire from 28-foot tower. the angle of depression from the tower to the fire is 11 degre
to the nearest foot, how far is the fire from the base of the tower
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To find the distance from the fire to the base of the tower, we can use trigonometry.
The angle of depression is the angle between the line of sight from the top of the tower to the fire, and the horizontal line. In this case, the angle of depression is 11 degrees.
Let's represent the distance from the base of the tower to the fire as "x".
From the information given, we can create a right triangle, where the distance from the top of the tower to the fire is the length of the opposite side, and the height of the tower is the length of the adjacent side.
Using trigonometry, we can use the tangent function to relate these sides:
tan(angle) = opposite/adjacent
tan(11 degrees) = x/28 feet
To solve for x, we can rearrange the equation:
x = tan(11 degrees) * 28 feet
Using a calculator, we can find:
x ≈ 5.12 feet
Therefore, to the nearest foot, the fire is approximately 5 feet away from the base of the tower.
To solve this problem, we can use trigonometry. The angle of depression is the angle between the horizontal line and the line of sight from the tower to the fire. In this case, the angle of depression is given as 11 degrees.
Let's assume that the distance from the base of the tower to the fire is x feet. We can use the tangent function to find the value of x.
Tangent is defined as the ratio of the length of the opposite side to the length of the adjacent side in a right triangle. In this case, the opposite side is the height of the tower (28 feet) and the adjacent side is the distance from the base of the tower to the fire (x feet).
Therefore, we have the equation:
tan(11 degrees) = 28/x
To solve for x, we need to isolate it on one side of the equation. We can do this by multiplying both sides of the equation by x:
x * tan(11 degrees) = 28
x = 28 / tan(11 degrees)
Using a calculator, we can evaluate the right side of the equation to find the value of x:
x ≈ 28 / tan(11 degrees) ≈ 158.68
Therefore, the fire is approximately 158.68 feet away from the base of the tower, rounded to the nearest foot.
Height / distance = tangent
so
distance = height / tangent
= 28 ft / tan(11°)
= ...