Question

note: figure not drawn to scale.
in the right triangle shown, what is the value of tan z?
a $\frac { sqrt { 3 } } { 34 }$
b $\frac { sqrt { 3 } } { 3 }$
c $sqrt { 3 }$
d $34 sqrt { 3 }$

Explanation:

Step1: Find the measure of angle \(Z\)

In a right - triangle, the sum of the two non - right angles is \(90^{\circ}\). Given one non - right angle \(X = 30^{\circ}\), then \(Z=90^{\circ}-30^{\circ} = 60^{\circ}\)

Step2: Recall the tangent function value

We know that \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\) in a right - triangle. Also, from the trigonometric values of special angles, \(\tan60^{\circ}=\sqrt{3}\)

Answer:

C. \(\sqrt{3}\)