Question

find the tangent of ∠e.

triangle with vertices d, e, c, right-angled at c. sides: dc = 30, ec = 16, de = 34

simplify your answer and write it as a proper fraction, improper fraction, or whole number.

tan(e) =

Explanation:

Step1: Recall tangent definition

For an acute angle in a right triangle, $\tan(\theta) = \frac{\text{opposite side}}{\text{adjacent side}}$

Step2: Identify sides for $\angle E$

Opposite side to $\angle E$: $DC = 30$; Adjacent side to $\angle E$: $EC = 16$

Step3: Substitute and simplify fraction

$\tan(E) = \frac{30}{16} = \frac{15}{8}$

Answer:

$\frac{15}{8}$