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

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

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 = (ED)/(FD)` (1)

`\cos F = (EF)/(FD)` (2)

If we know that
`\cos D = (12)/(13)` and
`FD = 39`, then the length of the line segment
`ED` is:

`ED = FD\cdot \cos D`

`ED = 39\cdot \left((12)/(13) \right)`

`ED = 36`

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