Question

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?

Answer 1

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