Exercise 45 Page 565

Practice makes perfect

a We are asked to draw three similar right triangles with a

5 0^{\circ}

angle. We will start with

△ A B C .

Let's start with drawing a segment

\overline{B A}

and the angle

∠ B

with a measure of

5 0^{\circ} .

Since we want $∠ A$ to be the right angle, we will draw a perpendicular segment that starts in point $A$ and intersects the dashed line we drew. The point of intersection will be the third vertex, $C .$

Next, we will draw two more triangles $△ M N P$ and $△ X Y Z .$ In these triangles $∠ M$ and $∠ X$ will be right angles, and $∠ N$ and $∠ Y$ will be $5 0^{\circ}$ angles.

b In this part, we are asked to complete the given table. To do this, we will measure appropriate sides with a ruler. Let's start with measuring the length of

\overline{A C} .

Next, we will measure the rest of sides in the same way.

Now, we will record these measures in the given table and evaluate the ratios.

Triangle	Length				Ratio
$A B C$	$A C$	$4.8$	$B C$	$6.3$	$\frac{A C}{B C}$	$\frac{4 . 8}{6 . 3} \approx 0.8$
$M N P$	$M P$	$2.4$	$N P$	$3.1$	$\frac{M P}{N P}$	$\frac{2 . 4}{3 . 1} \approx 0.8$
$X Y Z$	$X Z$	$2.5$	$Y Z$	$3.3$	$\frac{X Z}{Y Z}$	$\frac{2 . 5}{3 . 3} \approx 0.8$

c Looking at the table, we can see that the ratios are equal for each of the triangles. Therefore, we can assume that in right triangles with a

5 0^{\circ}

angle, the ratio of the leg opposite this angle to the hypotenuse is constant.

Subchapter links

Check Your Understanding p.562

Practice and Problem Solving p.562-565

H.O.T. Problems p.565

Standardized Test Practice p.566

Spiral Review p.566

Skills Review p.566

Exercise 45 Page 565

Hints

Check the answer

Practice exercises

Asses your skill