Marsha is using an 8-ft ladder to pick apples from a tree. If the bottom of the ladder is 3-ft from the bottom of the tree , calculate the angle of elevation to the nearest degree.Make sure to include diagram.
cos^-1 (3/8) = 68 degrees
To calculate the angle of elevation, we can use the tangent function. The tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is the height of the tree, which is the same as the height of the ladder, and the adjacent side is the distance from the bottom of the tree to the bottom of the ladder.
So, we have:
Tangent(angle) = height of the tree / distance to the tree
Let's calculate the height of the ladder. Since the ladder is 8 ft long and the bottom is 3 ft from the bottom of the tree, the height of the ladder is:
height of the ladder = 8 ft - 3 ft = 5 ft
Now we can plug in the values:
Tangent(angle) = 5 ft / 3 ft
To find the angle, we need to take the inverse tangent (or arctangent) of this ratio.
angle = arctan(5/3)
Using a calculator, we get:
angle ≈ 59.04 degrees
So, the angle of elevation is approximately 59 degrees.
Here's a diagram to help visualize the situation:
|
|
| height of
| the ladder
|
________________| <- ground
|_________________
bottom of the ladder bottom of the tree
Note: The diagram is not to scale.