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), \(tan(\frac{\pi }{2} )\)), 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,
\(tan(D)=\frac{EF}{ED} =\frac{12}{5}\).
