Question

give each trig ratio as a fraction in simplest form.
tan e =
○ 21/20
○ 29/21
○ 29/20

Explanation:

Step1: Recall tangent ratio

In a right triangle, the tangent of an acute angle is the ratio of the length of the opposite side to the length of the adjacent side. For angle \( E \) in right triangle \( DEF \) (right - angled at \( F \)):
The side opposite to angle \( E \) is \( DF = 21 \), and the side adjacent to angle \( E \) is \( EF=20 \).

Step2: Calculate \( \tan E \)

Using the formula for tangent, \( \tan E=\frac{\text{opposite}}{\text{adjacent}}=\frac{DF}{EF} \).
Substituting the values \( DF = 21 \) and \( EF = 20 \), we get \( \tan E=\frac{21}{20} \).

Answer:

A. \( 21/20 \)