Answer:
The value of the line segment [tex]ED[/tex] is 36.
Step-by-step explanation:
The hypotenuse represents the longest side in the right triangle. In this case, FD represents the hypotenuse as it is a multiple of 13. Based on the trigonometric relations described in the statements, we get the following relationships by definition of cosines:
[tex]\cos D = \frac{ED}{FD}[/tex] (1)
[tex]\cos F = \frac{EF}{FD}[/tex] (2)
If we know that [tex]\cos D = \frac{12}{13}[/tex] and [tex]FD = 39[/tex], then the length of the line segment [tex]ED[/tex] is:
[tex]ED = FD\cdot \cos D[/tex]
[tex]ED = 39\cdot \left(\frac{12}{13} \right)[/tex]
[tex]ED = 36[/tex]
The value of the line segment [tex]ED[/tex] is 36.
