a self supporting ladder placed so that the angle between the ladder and the ground is 75.5" can be used to test whether the ladder can support a certain load. The diagram represents a ladder placed next to a window that is 20feet above the ground. What is the length of the ladder ? Round to the nearest length.>
If the length is x, then
20/x = sin 75.5°
Now just solve for x.
20
To find the length of the ladder, we can use the tangent function.
1. Draw a right triangle with the ladder as the hypotenuse, the ground as the base, and the distance between the ground and the window as the height.
2. Label the angle between the ladder and the ground as 75.5°.
3. The tangent function is defined as the opposite side divided by the adjacent side. In this case, the opposite side is the height (20 feet) and the adjacent side is the base (the ground).
4. Use the tangent function to find the ratio of the opposite side to the adjacent side. tan(75.5°) = height / base.
5. Rearrange the equation to solve for the height. height = tan(75.5°) * base.
6. Substitute the values into the equation. Multiply tan(75.5°) by the base (which is the distance from the ground to the window, given in the problem) of 20 feet.
7. Calculate the value of the height using a scientific calculator or an online calculator.
8. Once you have found the height, you have the hypotenuse of the right triangle. This is the length of the ladder.
Round the length of the ladder to the nearest foot to get the final answer.