Question

question 18 (1 point)
for the given triangle, tan a is equal to which expression?
20 cm
a
15 cm
a) \frac{4}{3}
b) \frac{3}{5}
c) \frac{3}{4}
d) \frac{4}{5}

Explanation:

Step1: Recall the tangent formula

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). For angle \(A\), the opposite side is \(20\) cm and the adjacent side is \(15\) cm.

Step2: Calculate \(\tan A\)

\(\tan A=\frac{20}{15}\). Simplify the fraction \(\frac{20}{15}=\frac{4\times5}{3\times5}=\frac{4}{3}\) (divide numerator and denominator by their greatest common divisor \(5\)).

Answer:

A. \(\frac{4}{3}\)