Question

finding missing measures in regular polygons
a regular pentagon has a perimeter of 60 cm.
what is the measure of angle cbd?
36°
what is the length of segment cd?
6 cm
which trigonometric ratio can be used to compare bc
to cd using angle cbd?
sine
what is the approximate length of bc?
cm
s the approximate length of bd?
4.4 cm
7.4
8.3

Explanation:

Step1: Recall the sine ratio formula

The sine ratio is defined as \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). In right - triangle \(BCD\), \(\angle CBD = 36^{\circ}\), \(CD\) is the opposite side, and \(BC\) is the hypotenuse. So, \(\sin(\angle CBD)=\frac{CD}{BC}\).

Step2: Solve for \(BC\)

We know that \(CD = 6\) cm and \(\angle CBD=36^{\circ}\). From \(\sin(36^{\circ})=\frac{CD}{BC}\), we can rewrite it as \(BC=\frac{CD}{\sin(36^{\circ})}\).
Since \(\sin(36^{\circ})\approx0.5878\), then \(BC=\frac{6}{0.5878}\approx10.2\) cm.

Answer:

\(10.2\)