Chapter 8.4, Problem 11CE

To determine

To express: the PQ, PS and QR in terms of a.

Answer to Problem 11CE

The PQ, PS and QR in terms of a are 2a, $\sqrt{3}a$ and $\sqrt{2}a$ respectively.

Explanation of Solution

Given:

The triangle is shown below:

Calculation:

In triangle PQS,

  $\begin{array}{l}\sin 30°=\frac{QS}{PQ}\\ \frac{1}{2}=\frac{a}{PQ}\\ PQ=2a\end{array}$

And,

  $\begin{array}{l}\tan 30°=\frac{QS}{PS}\\ \frac{1}{\sqrt{3}}=\frac{a}{PS}\\ PS=\sqrt{3}a\end{array}$

In triangle QSR,

  $\begin{array}{l}\sin 45°=\frac{QS}{QR}\\ \frac{1}{\sqrt{2}}=\frac{a}{QR}\\ QR=\sqrt{2}a\end{array}$

Thus, the PQ, PS and QR in terms of a are 2a, $\sqrt{3}a$ and $\sqrt{2}a$ respectively.