A conveyor is used to lift paper to a shredder. The most efficient operating angle of elevation for the conveyor is 35.2°. The paper is to be elevated 16.0 m. What length of conveyor is needed?
same as your smokestack problem
sin 35.2 = 16/x
To find the length of the conveyor needed, we can use trigonometry and the concept of right triangles. Let's break down the problem into smaller steps:
Step 1: Visualize the problem
Imagine a right triangle where one angle is 35.2°, and the opposite side represents the vertical distance the paper needs to be elevated (16.0 m). The adjacent side of the triangle represents the length of the conveyor we are looking for.
Step 2: Identify the trigonometric ratio
Since we have the angle and the opposite side, we can use the tangent function to find the ratio between the opposite and adjacent sides. The tangent function is defined as the opposite side divided by the adjacent side.
Step 3: Apply the tangent function
Using the given angle of 35.2° and the opposite side of 16.0 m, we can write the equation:
tan(35.2°) = opposite / adjacent
Step 4: Solve for the adjacent side
Rearranging the equation, we have:
adjacent = opposite / tan(35.2°)
Step 5: Calculate
Plugging in the values, we get:
adjacent = 16.0 m / tan(35.2°)
Using a scientific calculator, find the value of the tangent of 35.2° and divide 16.0 m by that value to obtain the length of the conveyor needed.
Note: Ensure your calculator is set to the correct angle mode (degrees or radians) to get accurate results.
Once you perform the calculation, you will obtain the length of the conveyor needed to lift the paper to the shredder.