Question

In right triangle DEF, it is known that Cos D = (12/13) and Cos F = (5/13). If FD = 39, then DE = ? Hint, draw the right triangle.

Answer 1

Answer:

The value of the line segment $ED$ 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:

$\cos D = \frac{ED}{FD}$ (1)

$\cos F = \frac{EF}{FD}$ (2)

If we know that $\cos D = \frac{12}{13}$ and $FD = 39$, then the length of the line segment $ED$ is:

$ED = FD\cdot \cos D$

$ED = 39\cdot \left(\frac{12}{13} \right)$

$ED = 36$

The value of the line segment $ED$ is 36.