EXPLANATION
We can apply the Secan Secant Theorem in order to get the value of the side JF as shown as follows:
[tex]\bar{GroundE}\cdot\bar{GroundL}=\bar{GroundF}\cdot\bar{\text{GroundJ}}[/tex]
Replacing terms:
[tex]35\cdot(80+35)=40\cdot\bar{\text{GroundJ}}[/tex]
Adding numbers:
[tex]35\cdot115=40\cdot\bar{\text{GroundJ}}[/tex]
Dividing both sides by 40:
[tex]\frac{35\cdot115}{40}=\bar{\text{GroundJ}}[/tex]
Multiplying numbers and simplifying:
[tex]\frac{805}{8}=\text{GroundJ}[/tex]
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:
[tex]JF=\frac{805}{8}-40=60.625\text{ fe}et[/tex]
The answer is 60.6 feet
