Question

b
30°
c
8 ft
a
b
c
( b = ( 8 ) \tan ( 30 ^ { circ } ) )
( b = \frac { 8 } { \tan ( 30 ^ { circ } ) } )
( b = ( 8 ) sin ( 30 ^ { circ } ) )
( b = \frac { 8 } { sin ( 30 ^ { circ } ) } )

Explanation:

Step1: Recall the tangent function definition

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 30^{\circ}\), the opposite side to \(30^{\circ}\) is \(b\) and the adjacent side is \(8\) ft.
\(\tan(30^{\circ})=\frac{b}{8}\)

Step2: Solve for \(b\)

Multiply both sides of the equation \(\tan(30^{\circ})=\frac{b}{8}\) by \(8\).
\(b = 8\tan(30^{\circ})\)

Answer:

\(b=(8)\tan(30^{\circ})\)