Chapter 9.7, Problem 2PSA

a

To determine

To find: The missing sides of the triangle a side = 6 of y1$30°-60°-90°$ triangle is given.

Answer to Problem 2PSA

The missing sides are 3$\frac{12}{\sqrt{3}}$ and $\frac{6}{\sqrt{3}}$

Explanation of Solution

Given information Right triangle of $30°-60°-90°$

Since, sides are x, $\text{x}\sqrt{3}$ , 2x

And here, we have given

  $\begin{array}{l}x\sqrt{3}=6\\ x=\frac{6}{\sqrt{3}}\end{array}$

Hence, missing sides are $\frac{12}{\sqrt{3}}$ and $\frac{6}{\sqrt{3}}$.

b

To determine

To find: The missing sides of the triangle a side = 15 of $30°-60°-90°$ triangle is given.

Answer to Problem 2PSA

The missing sides are $7.5\sqrt{3}$ and 7.5

Explanation of Solution

Given information Right triangle of $30°-60°-90°$

Since, sides are x, $\text{x}\sqrt{3}$ , 2x

Here we have given that

  $\begin{array}{l}2x=15\\ x=7.5\end{array}$

Hence, missing sides are $7.5\sqrt{3}$ and 7.5

c

To determine

To find: The missing sides of the triangle a side = 15 of $30°-60°-90°$ triangle is given.

Answer to Problem 2PSA

The missing sides are $5\sqrt{3}\text{ and}10\sqrt{3}$

Explanation of Solution

Given information Right triangle of $30°-60°-90°$

Since, sides are x, $\text{x}\sqrt{3}$ , 2x

Here we have given that

  $\begin{array}{l}x\sqrt{3}=15\\ x=\frac{15}{\sqrt{3}}=5\sqrt{3}\end{array}$

Hence, missing sides are

  $5\sqrt{3}\text{ and }10\sqrt{3}$

d

To determine

To find: The missing sides of the triangle a side = 7 of $30°-60°-90°$ triangle is given.

Answer to Problem 2PSA

The missing sides are $\frac{1}{3}\left(7\sqrt{3}\right)\text{and}\frac{2}{3}\left(7\sqrt{3}\right)$

Explanation of Solution

Given information Right triangle of $30°-60°-90°$

Since, sides are x, $\text{x}\sqrt{3}$ , 2x

Hence, missing sides are

  $\frac{1}{3}\left(7\sqrt{3}\right)\text{and}\frac{2}{3}\left(7\sqrt{3}\right)$