Chapter 8.6, Problem 12CE

To determine

To prove: the value of $\sin 30°$ is exactly 0.5.

Answer to Problem 12CE

The value of $\sin 30°$ is exactly 0.5.

Explanation of Solution

Calculation:

Consider an equilateral triangle with perpendicular from one vertex and side 2a as shown below:

  

Determine the perpendicular PE as follows:

  $\begin{array}{c}FP=\sqrt{{\left(2a\right)}^2-{\left(a\right)}^2}\\ =\sqrt{4a^2-a^2}\\ =\sqrt{3a^2}\\ =\sqrt{3}a\end{array}$

Consider triangle EFP ,

  $\begin{array}{c}\sin 30°=\frac{FP}{FE}\\ =\frac{a}{2a}\\ =0.5\end{array}$

Thus, the value of $\sin 30°$ is exactly 0.5.