Question

Express tan DD as a fraction in simplest terms.
D
E
F
16
12
20
Answer
Attempt 1 out of 2

e has a 90 degree angle

Answer 1

To express \(\tan D\) as a fraction in simplest terms, we can first identify the sides of triangle DEF, given the angles and the lengths. Assuming \(D\) is one of the angles in a right triangle and that \(\angle E\) is the right angle (90 degrees), we can use the opposite side and adjacent side to angle \(D\).

From your message, we assume:

- \(DE = 12\) (adjacent to \(\angle D\))
- \(EF = 16\) (opposite to \(\angle D\))
- The hypotenuse \(DF = 20\)

The tangent of angle \(D\) is defined as the ratio of the opposite side to the adjacent side:

\[
\tan D = \frac{\text{opposite}}{\text{adjacent}} = \frac{EF}{DE} = \frac{16}{12}
\]

Now, we can simplify this fraction:

\[
\tan D = \frac{16 \div 4}{12 \div 4} = \frac{4}{3}
\]

Thus, the fraction representing \(\tan D\) in simplest terms is:

\[
\boxed{\frac{4}{3}}
\]