See figure 2.19. Find RP and PS using the information given in \(\triangle PSR\).
Figure: In \(\triangle PSR\), \(\angle S = 90^\circ\), \(\angle P = 30^\circ\) and RS = 6.
Answer: RP = 12 and PS = \(6\sqrt{3}\)
\(\triangle PSR\) is a \(30^\circ\)–\(60^\circ\)–\(90^\circ\) triangle (\(\angle R = 60^\circ\)), with hypotenuse RP.
Side opposite the \(30^\circ\) angle = half the hypotenuse:
\[RS = \frac{1}{2} RP \Rightarrow RP = 2 \times 6 = 12\]Side opposite the \(60^\circ\) angle = \(\frac{\sqrt{3}}{2}\) × hypotenuse:
\[PS = \frac{\sqrt{3}}{2} \times 12 = 6\sqrt{3}\]Log in or create a free account to answer this question.
