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 20 feet above the ground. What is the length of the ladder? Round to the nearest tenth.
To find the length of the ladder, we can use the trigonometric ratio known as sine.
In this case, we are given the angle between the ladder and the ground, which is 75.5°. We also know that the height of the window is 20 feet.
The trigonometric ratio used to find the height of a right-angled triangle when the angle is known is: sine.
In this case, we can use sine because we have the opposite side (20 feet) and we want to find the hypotenuse (length of the ladder).
The formula for sine is:
sin(θ) = opposite / hypotenuse
Rearranging the formula to solve for the hypotenuse:
hypotenuse = opposite / sin(θ)
Using this formula, we can substitute the given values to find the length of the ladder:
hypotenuse = 20 / sin(75.5°)
Now, we can calculate the length of the ladder using a calculator:
hypotenuse ≈ 20 / 0.9781 ≈ 20.4689 feet
So, the length of the ladder is approximately 20.5 feet (rounded to the nearest tenth).
I don't see any diagram but by a simple trig ratio, we have
cos 75.5 = 20/L
L = 20/cos75.5 = appr 79.9 ft
Wow, a ladder to go up about 8 stories high???