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Two angles are supplementary. The smaller angle is $\text{36\xb0}$ less than the larger angle. Find the measures of both angles.
Two angles are complementary. The smaller angle is $\text{34\xb0}$ less than the larger angle. Find the measures of both angles.
62°, 28°
Two angles are complementary. The larger angle is $\text{52\xb0}$ more than the smaller angle. Find the measures of both angles.
Use the Properties of Triangles In the following exercises, solve using properties of triangles.
The measures of two angles of a triangle are $\text{26\xb0}$ and $\text{98\xb0}.$ Find the measure of the third angle.
56°
The measures of two angles of a triangle are $\text{61\xb0}$ and $\text{84\xb0}.$ Find the measure of the third angle.
The measures of two angles of a triangle are $\text{105\xb0}$ and $\text{31\xb0}.$ Find the measure of the third angle.
44°
The measures of two angles of a triangle are $\text{47\xb0}$ and $\text{72\xb0}.$ Find the measure of the third angle.
One angle of a right triangle measures $\text{33\xb0}.$ What is the measure of the other angle?
57°
One angle of a right triangle measures $\text{51\xb0}.$ What is the measure of the other angle?
One angle of a right triangle measures $22.5\xb0.$ What is the measure of the other angle?
67.5°
One angle of a right triangle measures $36.5\xb0.$ What is the measure of the other angle?
The two smaller angles of a right triangle have equal measures. Find the measures of all three angles.
45°, 45°, 90°
The measure of the smallest angle of a right triangle is $\text{20\xb0}$ less than the measure of the other small angle. Find the measures of all three angles.
The angles in a triangle are such that the measure of one angle is twice the measure of the smallest angle, while the measure of the third angle is three times the measure of the smallest angle. Find the measures of all three angles.
30°, 60°, 90°
The angles in a triangle are such that the measure of one angle is $\text{20\xb0}$ more than the measure of the smallest angle, while the measure of the third angle is three times the measure of the smallest angle. Find the measures of all three angles.
Find the Length of the Missing Side In the following exercises, $\text{\Delta}ABC$ is similar to $\text{\Delta}XYZ.$ Find the length of the indicated side.
On a map, San Francisco, Las Vegas, and Los Angeles form a triangle whose sides are shown in
[link] . The actual distance from Los Angeles to Las Vegas is
$270$ miles.
Find the distance from Los Angeles to San Francisco.
351 miles
Find the distance from San Francisco to Las Vegas.
Use the Pythagorean Theorem In the following exercises, use the Pythagorean Theorem to find the length of the hypotenuse.
Find the Length of the Missing Side In the following exercises, use the Pythagorean Theorem to find the length of the missing side. Round to the nearest tenth, if necessary.
In the following exercises, solve. Approximate to the nearest tenth, if necessary.
A $\text{13-foot}$ string of lights will be attached to the top of a $\text{12-foot}$ pole for a holiday display. How far from the base of the pole should the end of the string of lights be anchored?
5 feet
Pam wants to put a banner across her garage door to congratulate her son on his college graduation. The garage door is $12$ feet high and $16$ feet wide. How long should the banner be to fit the garage door?
Chi is planning to put a path of paving stones through her flower garden. The flower garden is a square with sides of $10$ feet. What will the length of the path be?
14.1 feet
Brian borrowed a $\text{20-foot}$ extension ladder to paint his house. If he sets the base of the ladder $6$ feet from the house, how far up will the top of the ladder reach?
Building a scale model Joe wants to build a doll house for his daughter. He wants the doll house to look just like his house. His house is $30$ feet wide and $35$ feet tall at the highest point of the roof. If the dollhouse will be $2.5$ feet wide, how tall will its highest point be?
2.9 feet
Measurement A city engineer plans to build a footbridge across a lake from point $\text{X}$ to point $\text{Y},$ as shown in the picture below. To find the length of the footbridge, she draws a right triangle $\text{XYZ},$ with right angle at $\text{X}.$ She measures the distance from $\text{X}$ to $\text{Z},800$ feet, and from $\text{Y}$ to $\text{Z},\mathrm{1,000}$ feet. How long will the bridge be?
Write three of the properties of triangles from this section and then explain each in your own words.
Answers will vary.
Explain how the figure below illustrates the Pythagorean Theorem for a triangle with legs of length $3$ and $4.$
ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.
ⓑ What does this checklist tell you about your mastery of this section? What steps will you take to improve?
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