If the length of the cable from L to E is 80 feet, E to the ground is 35 feet, and F to the ground is 40 feet, what is the length of the cable from J to F?

Question

asked Dec 16, 2023 88.8k views

1 Answer

Cubski · Answer 1 · 2023-12-21T02:19:04+0000

EXPLANATION

We can apply the Secan Secant Theorem in order to get the value of the side JF as shown as follows:

$\bar{GroundE}\cdot\bar{GroundL}=\bar{GroundF}\cdot\bar{\text{GroundJ}}$

Replacing terms:

$35\cdot(80+35)=40\cdot\bar{\text{GroundJ}}$

Adding numbers:

$35\cdot115=40\cdot\bar{\text{GroundJ}}$

Dividing both sides by 40:

$(35\cdot115)/(40)=\bar{\text{GroundJ}}$

Multiplying numbers and simplifying:

$(805)/(8)=\text{GroundJ}$

As ground to J is the sum of JF + F to ground, we can isolate the measure of the segment JF as shown as follows:

$JF=(805)/(8)-40=60.625\text{ fe}et$

The answer is 60.6 feet