Answer :

Answer:

tan D = 12/5

Step-by-step explanation:

Recall trigonometric ratios or SOH - CAH - TOA. The reference angle whose value inside of the parenthesis in any trigonometric function (i.e. sin(x), cos(23 deg), [tex]tan(\frac{\pi }{2} )[/tex]), is used when identifying the adjacent and opposite side lengths of the angle.

  • Sine is the ratio of the opposite side length and the hypotenuse.
  • Cosine is the ratio of the adjacent side and the hypotenuse
  • Tangent is the ratio of the opposite and the adjacent side length.

In this case, D is the reference angle, so line EF is the opposite side length and line ED is the adjacent one. So,

[tex]tan(D)=\frac{EF}{ED} =\frac{12}{5}[/tex].