A 38 ft long ladder is leaning against an embankment inclined at 60 deg. to the horizontal. If the bottom of the ladder is 15 ft from the embankment, what is the distance from the top of the ladder down to the embankment to the ground?
Apply the Pythagorean theorem, a^2 + b^2 = c^2
15^2 + x^2 = 38^2
Solve for x.
To find the distance from the top of the ladder down to the embankment to the ground, we can use trigonometry.
Let's label the distance we're trying to find as "x".
First, let's draw a diagram to visualize the problem. We have a right triangle formed by the ladder, the ground, and the embankment.
The ladder is the hypotenuse of the triangle, the distance from the bottom of the ladder to the embankment is the adjacent side, and the distance from the embankment to the ground is the opposite side.
Now, we can use the trigonometric ratio for the sine function:
sine(angle) = opposite/hypotenuse
In this case, the angle is 60 degrees, the opposite side is x, and the hypotenuse is 38 ft.
So we have:
sin(60°) = x/38
To find x, we can rearrange the equation:
x = sin(60°) * 38
Now we just need to calculate the value of sin(60°) and multiply it by 38:
x ≈ 0.866 * 38
x ≈ 32.908
Therefore, the distance from the top of the ladder down to the embankment to the ground is approximately 32.908 ft.