Chapter 9.4, Problem 1PSA

(a)

To determine

To find: The third unknown side if the other two side is given i.e. $x=4\text{ and }y=5$ .

Answer to Problem 1PSA

The third unknown side is $\sqrt{41}$ .

Explanation of Solution

Given information :

  $x=4\text{ and }y=5$

Formula used :

  $r^2=x^2+y^2$

Calculation :

  $\begin{array}{l}{r}^2=4^2+5^2\\ =16+25\\ =41\\ \Rightarrow r=\sqrt{41}\end{array}$

(b)

To determine

To find: The third unknown side if the other two side is given i.e. $x=15\text{ \& }r=17$ .

Answer to Problem 1PSA

The third unknown side is 8.

Explanation of Solution

Given information :

  $x=15\text{ and }r=17$

Formula used :

  $r^2=x^2+y^2$

Calculation :

  $\begin{array}{l}{17}^2={15}^2+y^2\\ \Rightarrow y^2={17}^2-{15}^2=289-225\\ \Rightarrow y=\sqrt{64}=8\end{array}$

(c)

To determine

To find: The third unknown side if the other two side is given i.e. $y=9\text{ and }r=15$ .

Answer to Problem 1PSA

The third unknown side is 12.

Explanation of Solution

Given information :

  $y=9\text{ and }r=15$

Formula used :

  $r^2=x^2+y^2$

Calculation :

  $\begin{array}{l}{15}^2=x^2+9^2\\ \Rightarrow x^2={15}^2-9^2=225-81=144\\ \Rightarrow x=\sqrt{144}=12\end{array}$

(d)

To determine

To find: The third unknown side if the other two side is given i.e. $x=12\text{ and }r=13$ .

Answer to Problem 1PSA

The third unknown side is 5.

Explanation of Solution

Given information :

  $x=12\text{ and }r=13$

Formula used :

  $r^2=x^2+y^2$

Calculation :

  $\begin{array}{l}{13}^2={12}^2+y^2\\ \Rightarrow y^2={13}^2-{12}^2=169-144=25\\ \Rightarrow y=\sqrt{25}=5\end{array}$

(e)

To determine

To find: The third unknown side if the other two side is given i.e. $x=5\text{ and }y=5\sqrt{3}$ .

Answer to Problem 1PSA

The third unknown side is 10.

Explanation of Solution

Given information :

  $x=5\text{ and }y=5\sqrt{3}$

Formula used :

  $r^2=x^2+y^2$

Calculation :

  $\begin{array}{l}{r}^2=5^2+{\left(5\sqrt{3}\right)}^2\\ \Rightarrow r^2=25+75=100\\ \Rightarrow r=\sqrt{100}=10\end{array}$

(f)

To determine

To find: The third unknown side if the other two side is given i.e. $x=5\text{ and }r=\sqrt{29}$ .

Answer to Problem 1PSA

The third unknown side is 2.

Explanation of Solution

Given information :

  $x=5\text{ and }r=\sqrt{29}$

Formula used :

  $r^2=x^2+y^2$

Calculation :

  $\begin{array}{l}{\left(\sqrt{29}\right)}^2=5^2+y^2\\ \Rightarrow y^2=29-25=4\\ \Rightarrow y=\sqrt{4}=2\end{array}$

(g)

To determine

To find: The third unknown side if the other two side is given i.e. $x=2\sqrt{5} \text{and }r=\sqrt{38}$ .

Answer to Problem 1PSA

The third unknown side is $3\sqrt{2}$ .

Explanation of Solution

Given information :

  $x=2\sqrt{5} \text{and }r=\sqrt{38}$

Formula used :

  $r^2=x^2+y^2$

Calculation :

  $\begin{array}{l}{\left(\sqrt{38}\right)}^2={\left(2\sqrt{5}\right)}^2+y^2\\ \Rightarrow y^2=38-20=18\\ \Rightarrow y=\sqrt{18}=3\sqrt{2}\end{array}$