Question

use the sliders to solve the triangle given c = 40 and b = 35°. 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)°
b. \frac{40}{cos(35)°}
c. 40 sin (35)°
d. \frac{sin(35)°}{40}
e. 40 cos (35)°

Explanation:

Step1: Recall the sine formula

In a right - triangle, \(\sin B=\frac{b}{c}\), where \(B\) is an acute angle, \(b\) is the side opposite to angle \(B\), and \(c\) is the hypotenuse.

Step2: Substitute the given values

Given \(c = 40\) and \(B=35^{\circ}\). From \(\sin B=\frac{b}{c}\), we can solve for \(b\). Rearranging the formula gives \(b = c\sin B\).
Substituting \(c = 40\) and \(B = 35^{\circ}\), we get \(b=40\sin(35)^{\circ}\)

Answer:

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