A guy wire attached to the top of an electric pole makes a 700 angle with the level ground. At a point 25 feet from the guy wire (farther away from the pole), the angel of elevation to the top of the pole is 420. How long is the guy wire?

absurd angles, check your typing.

did you mean 70° instead of 700 ?

To solve this problem, we can begin by drawing a diagram to visualize the situation. Let's represent the electric pole as a vertical line and the guy wire as a diagonal line that makes an angle of 70 degrees with respect to the ground.

Now, let's label the relevant information:
- The angle of the guy wire with respect to the ground is 70 degrees.
- At a point 25 feet from the guy wire (farther away from the pole), the angle of elevation to the top of the pole is 42 degrees.

To find the length of the guy wire, we can use trigonometry. Specifically, we can use the tangent function, which relates the opposite side of a right triangle to the adjacent side.

In this case, we can consider the right triangle formed by the ground, the guy wire, and the vertical line from the top of the pole to the point 25 feet away from the guy wire.

Let's denote:
- The length of the guy wire as 'x'.

Now, let's use the tangent function to calculate the length of the guy wire:
We have tan(70) = Opposite / Adjacent
tan(70) = x / 25

To solve for x, we can multiply both sides of the equation by 25:
25 * tan(70) = x

Using a scientific calculator, we can determine that tan(70) ≈ 2.74747741945462.

Therefore, the length of the guy wire 'x' is:
x ≈ 25 * 2.74747741945462 ≈ 68.6879354864

So, the length of the guy wire is approximately 68.69 feet.