Question

in the figure, two poles are 25 m and 40 m high. a cable 29 m long joins the tops of the poles. find the distance between the poles. the distance between the poles is □ (round to the nearest tenth as needed)

Explanation:

Step1: Find the vertical difference between the poles

The vertical difference \( h=40 - 25=15\) m.

Step2: Apply the Pythagorean theorem

Let the distance between the poles be \( d\). According to the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c = 29\) (the length of the cable) and \(a = 15\) (vertical difference). We need to find \(b\) (horizontal distance).

$$d=\sqrt{29^{2}-15^{2}}$$

$$d=\sqrt{(29 + 15)(29-15)}$$

(using \(a^{2}-b^{2}=(a + b)(a - b)\))

$$d=\sqrt{44\times14}$$

$$d=\sqrt{616}$$

$$d = 24.819347\approx24.8$$

Answer:

\(24.8\) m