Question

there is a right triangle with right angle at c, side length 5 cm (opposite to angle a), side b (adjacent to angle a), hypotenuse 10 cm, and angle at a is 30°. the options are: tan(30°) = 5/b; tan(30°) = b/5; tan(30°) = 10/b; tan(30°) = b/10

Explanation:

Step1: Recall the tangent function definition

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\).

Step2: Identify the sides relative to angle \(A\)

For angle \(A = 30^{\circ}\), the side opposite to \(A\) is \(5\) cm and the side adjacent to \(A\) is \(b\) cm.
So, \(\tan(30^{\circ})=\frac{5}{b}\)

Answer:

\(\tan(30^{\circ})=\frac{5}{b}\) (the first option)