Question

a 60.4 m long thick wire attaches 29.6 m up a radio tower pole. the wire then attaches into the ground to steady the pole in windy weather. how far from the pole is the wire stuck into the ground if it is pulled taut?

52.6 m
56.2 m
65.2 m
62.5 m

Explanation:

Identify the geometric model

The radio tower pole, the ground, and the taut wire form a right-angled triangle. The pole is perpendicular to the ground, creating a \(90^\circ\) angle.

Define the given values

Let the length of the wire (hypotenuse) be \(c = 60.4\text{ m}\).
Let the height up the pole where the wire attaches (one leg) be \(a = 29.6\text{ m}\).
Let the distance from the pole to where the wire is stuck into the ground (the other leg) be \(b\).

Apply the Pythagorean theorem

Using the Pythagorean Theorem for a right triangle:

$$a^2 + b^2 = c^2$$

Solve for the unknown leg \(b\):

$$b = \sqrt{c^2 - a^2}$$

Calculate the numerical value

Substitute the given values into the equation:

$$b = \sqrt{60.4^2 - 29.6^2}$$

$$b = \sqrt{3648.16 - 876.16}$$

$$b = \sqrt{2772}$$

$$b \approx 52.65\text{ m}$$

Rounding to the nearest tenth gives \(52.6\text{ m}\).

Answer:

• (A) 52.6 m (Correct answer)
• (B) 56.2 m
• (C) 65.2 m
• (D) 62.5 m