Find the length of an inclined plane that will reach a platform 8ft high and form 16degree with the ground
To find the length of the inclined plane, we can use the concept of trigonometry and the relationship between the length, height, and angle of inclination.
In this case, we know the height of the platform is 8 ft and the angle of inclination is 16 degrees.
Step 1: Visualize the triangle formed by the inclined plane, the height, and the ground.
Step 2: Identify the sides of the triangle:
- The height of the platform represents the opposite side (O).
- The length of the inclined plane represents the hypotenuse (H).
- The distance on the ground represents the adjacent side (A).
Step 3: Use the trigonometric formula:
- In this case, we have the opposite side (O) and the angle (θ) given. We need to find the hypotenuse (H).
- The trigonometric function that relates these values is the sine (sin) function: Sin(θ) = O/H.
Step 4: Calculate the length of the inclined plane:
- Rearrange the formula to isolate the hypotenuse (H): H = O / sin(θ).
- Substitute the given values: H = 8 ft / sin(16°).
Step 5: Calculate the length:
- Use a calculator (or computer application) that has trigonometric functions.
- Calculate sin(16°) and divide 8 ft by that value.
- The result will be the length of the inclined plane needed to reach the platform.
Keep in mind that the length of the inclined plane might need to be adjusted to allow for a safe and practical pathway.