a 30 foot ladder leaning against a vertical wall makes an angle of 81 degrees with the ground how far from the base of the pole is the surveyor?

the question was suppose to be how far from the base of the wall is the foot of the ladder

cos 81 = x/30

To find the distance from the base of the pole to the surveyor, we can use trigonometry. In this case, we can use the tangent function.

First, let's define the variables:
- Let A be the angle between the ladder and the ground (81 degrees).
- Let B be the angle between the ladder and the wall.
- Let x be the distance from the base of the pole to the surveyor.

Since we have the angle A and the length of the ladder (30 feet), we can use the tangent function (tan) to find x.

The tangent of angle A is defined as the ratio of the length of the side opposite angle A (height) to the length of the side adjacent to angle A (distance from the base to the surveyor):
tan(A) = height / x

We know the length of the ladder is the height, so we can rewrite the equation as:
tan(A) = 30 / x

Now, we can substitute the value of A (81 degrees) into the equation:
tan(81) = 30 / x

To find the value of x, we need to rearrange the equation:
x = 30 / tan(81)

Using a scientific calculator, we can evaluate the tangent of 81 degrees and calculate x:
x ≈ 30 / 5.67128181961771

Therefore, the surveyor is approximately 5.29 feet away from the base of the pole.