guy wire is attached to a pole for support. If the angle of elevation to the pole is 67° and the wire is attached to the ground at a point 137 feet from the base of the pole, what is the height of the pole (round to 2 decimal places)?

h/137 = tan 67°

And away you go...

To find the height of the pole, we can use trigonometry. Let's call the height of the pole "h".

We know that the angle of elevation to the pole is 67°. This means that if we draw a right triangle with the base being the distance from the wire attachment point to the base of the pole (137 feet) and the height being "h", the angle between the base and the hypotenuse is 67°.

Using the trigonometric function tangent (tan), we can set up the following equation:

tan(67°) = h / 137

To solve for "h", we can isolate it by multiplying both sides of the equation by 137:

h = 137 * tan(67°)

Using a calculator, we can find that:

h ≈ 289.83 feet

Therefore, the height of the pole is approximately 289.83 feet (rounded to 2 decimal places).

To solve this problem, we can use trigonometry and specifically the tangent function.

The tangent of an angle is defined as the ratio of the opposite side to the adjacent side.

In this case, the height of the pole is the opposite side and the distance from the base of the pole to the point where the wire is attached to the ground is the adjacent side.

Let's label the height of the pole as h and the distance from the base of the pole to the point where the wire is attached to the ground as x.

We know that the angle of elevation to the pole is 67° and the distance from the base of the pole to the attachment point on the ground is 137 feet.

Using the tangent function, we can set up the following equation:

tan(67°) = h / x

Now we can solve for h:

h = x * tan(67°)

Substituting x = 137 feet and using a calculator to find the tangent of 67°, we have:

h = 137 * tan(67°)

Calculating this expression, we find:

h ≈ 283.27 feet

Therefore, the height of the pole is approximately 283.27 feet.

The answer is 154 ft