A ladder 35 foot long is leaning against an embankment, inclined 62.5 degrees to the horizontal. if the bottom of the ladder is 10.2 feet from the embankment, what is the distance from the top of the ladder down to the embankment to the ground?

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To solve this problem, we can use trigonometry. Let's denote the distance from the top of the ladder down to the embankment to the ground as "x".

Since the ladder is leaning against the embankment, we can form a right triangle with the ladder as the hypotenuse and the bottom of the ladder, the embankment, and the distance from the top of the ladder down to the embankment as the other sides.

Using the sine function, we can write:

sin(62.5°) = x / 35

To find the value of x, we can rearrange the equation:

x = 35 * sin(62.5°)

Using a calculator, we can calculate the value of sin(62.5°) to be approximately 0.8910.

Substituting this value into the equation:

x = 35 * 0.8910

x ≈ 31.19

Therefore, the distance from the top of the ladder down to the embankment to the ground is approximately 31.19 feet.

To find the distance from the top of the ladder down to the embankment to the ground, we need to use trigonometry.

Let's label the distance we want to find as "x".

We have the length of the ladder (35 feet) and the angle it makes with the horizontal (62.5 degrees), and also the horizontal distance from the bottom of the ladder to the embankment (10.2 feet).

We can use the sine function to relate the angle and the distances:
sin(angle) = opposite/hypotenuse

In this case, the opposite side is the distance we want to find (x) and the hypotenuse is the length of the ladder (35 feet).

So, we have:
sin(62.5 degrees) = x/35

Now, we can calculate x:
x = sin(62.5 degrees) * 35

Using a calculator, we find:
x ≈ 30.86 feet

Therefore, the distance from the top of the ladder down to the embankment to the ground is approximately 30.86 feet.