Chapter 8.3, Problem 45PPS

(a)

To determine

To draw: Three similar right triangles.

Explanation of Solution

Given information: The base angle is $50°$ .

Drawing: Using protractor to draw $50°$ and $90°$ angle. And ruler is used to measure the side length.

(b)

To determine

To fill: The given empty table.

Answer to Problem 45PPS

The following table is been filled.

  $\begin{array}{ccccccc}Triangles& & & Length& & & Ratio\\ ABC& AC& 3.5& BC& 4.5& \frac{AC}{BC}& 0.7778\\ MNP& MP& 4.6& NP& 6& \frac{MP}{NP}& 0.7667\\ XYZ& XZ& 5.9& YZ& 7.3& \frac{XZ}{YZ}& 0.8082\end{array}$

Explanation of Solution

Given information: The diagrams from part (a),

Calculation: The table has been filled. The ratio and length is been given in the following table.

  $\begin{array}{ccccccc}Triangles& & & Length& & & Ratio\\ ABC& AC& 3.5& BC& 4.5& \frac{AC}{BC}& 0.7778\\ MNP& MP& 4.6& NP& 6& \frac{MP}{NP}& 0.7667\\ XYZ& XZ& 5.9& YZ& 7.3& \frac{XZ}{YZ}& 0.8082\end{array}$

(c)

To determine

To conjecture: The ratio of the leg opposite the $50°$ angle to the hypotenuse in any right triangle with an angle measuring $50°$ .

Answer to Problem 45PPS

The ratio of sides differs because there is a rounding error in measurements.

Explanation of Solution

Given information: The following table shows the ratios of the triangles.

  $\begin{array}{ccccccc}Triangles& & & Length& & & Ratio\\ ABC& AC& 3.5& BC& 4.5& \frac{AC}{BC}& 0.7778\\ MNP& MP& 4.6& NP& 6& \frac{MP}{NP}& 0.7667\\ XYZ& XZ& 5.9& YZ& 7.3& \frac{XZ}{YZ}& 0.8082\end{array}$

These triangles are similar so their ratios should be the same for all. But due to rounding error, there is a difference in all ratios. The accurate ratio is about $0.7660$ .