Question

use the sliders to solve the triangle given ( c = 40 ) and ( b = 35 ^ { circ } ). determine the exact value of side ( b ).
use the interactive figure to find your answer. use the left and right arrow keys to move along a slider as needed.
click here to launch the interactive figure.
choose the correct answer below.
a. ( 40 \tan ( 35 ) ^ { circ } )
b. ( 40 cos ( 35 ) ^ { circ } )
c. ( 40 sin ( 35 ) ^ { circ } )
d. ( \frac { 40 } { cos ( 35 ) ^ { circ } } )
e. ( \frac { 40 } { sin ( 35 ) ^ { circ } } )

Explanation:

Step1: Recall the sine function definition

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, \(\theta = B = 35^{\circ}\), the hypotenuse \(c = 40\), and the side opposite to angle \(B\) is \(b\).

Step2: Substitute into the sine formula

We have \(\sin(35^{\circ})=\frac{b}{40}\).

Step3: Solve for \(b\)

Multiply both sides of the equation \(\sin(35^{\circ})=\frac{b}{40}\) by \(40\). So, \(b = 40\sin(35^{\circ})\).

Answer:

C. \(40\sin(35)^{\circ}\)