A drainage pipe has an angle of elevation of 2.3° over a distance of 102 feet. What is the rise in height of the pipe?
To find the rise in height of the pipe, we need to use trigonometry.
The angle of elevation, given as 2.3°, represents the angle between the horizontal ground and the line of sight to the top of the pipe.
Let's call the rise in height of the pipe as "h".
Using the tangent function, we can set up the equation:
tan(2.3°) = h / 102 feet
Solving for h, we multiply both sides of the equation by 102 feet:
h = tan(2.3°) * 102 feet
Using a calculator, we find that tan(2.3°) ≈ 0.0402.
Plugging in this value, the rise in height of the pipe is:
h ≈ 0.0402 * 102 feet ≈ 4.10 feet
So, the rise in height of the pipe is approximately 4.10 feet.
To find the rise in height of the pipe, we can use the trigonometric function tangent.
The tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side. In this case, the opposite side represents the rise in height of the pipe, and the adjacent side represents the distance of 102 feet.
The formula for tangent is given as:
tangent(angle) = opposite/adjacent
To find the rise in height, we can rearrange the formula:
opposite = tangent(angle) * adjacent
Substituting the given values:
opposite = tangent(2.3°) * 102 feet
Now we can calculate the rise in height using a scientific calculator or an online calculator.
opposite ≈ 2.317 * 102 feet ≈ 237.0346 feet
Therefore, the rise in height of the pipe is approximately 237.0346 feet.
To find the rise in height of the pipe, we can use trigonometry.
The angle of elevation, in this case, is 2.3°. This angle represents the angle between the horizontal ground and the line of sight towards the top of the drainage pipe.
The distance along the ground is given as 102 feet.
To find the rise in height, we need to use the tangent function. The tangent of an angle is defined as the ratio of the opposite side to the adjacent side in a right triangle.
In this case, the rise in height is the opposite side and the distance along the ground is the adjacent side. Therefore, we can use the formula:
tangent(angle) = opposite / adjacent
tangent(2.3°) = rise / 102
To solve for the rise, we rearrange the equation:
rise = tangent(2.3°) * 102
Now we can calculate the rise in height of the pipe using a calculator:
rise = tan(2.3°) * 102
rise ≈ 4.43 feet
Therefore, the rise in height of the drainage pipe is approximately 4.43 feet.