Chapter 9.4, Problem 43E

To determine

To graph the given number $\sqrt{34}$on a number line using a right triangle.

Answer to Problem 43E

The diagram of the right angles based on the previous right triangle with the help of formula:

  

Explanation of Solution

Given:

The given number is $\sqrt{34}$ .

Calculation:

Draw the right angles based on the previous right triangle with the help of formula:

  $\begin{array}{l}$ {\text{Hypotenuse}}^2={\text{ (side1)}}^2+{(side2)}^2$\Rightarrow \text{Hypotenuse}=\text{}\sqrt{{\text{1}}^2+{\text{ 1}}^2}=\sqrt{2}\end{array}$

Similarly, the next hypotenuse values could be found.

The given number can be drawn on a line using right triangles as follows:

First draw a straight line with distance of $1$ unit horizontally and vertically to get the value of $\sqrt{2}$ , such that the diagonal distance can be calculated using the formula,

  $\begin{array}{l}$ {(Diagonal)}^2={(Side1)}^2+{(Side2)}^2$\sqrt{2}=\sqrt{{(1)}^2+{(1)}^2}\end{array}$

Similarly continue the process until get $\sqrt{34}$ .