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Two angles are supplementary. The smaller angle is 36° less than the larger angle. Find the measures of both angles.

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Two angles are complementary. The smaller angle is 34° less than the larger angle. Find the measures of both angles.

62°, 28°

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Two angles are complementary. The larger angle is 52° more than the smaller angle. Find the measures of both angles.

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Use the Properties of Triangles In the following exercises, solve using properties of triangles.

The measures of two angles of a triangle are 26° and 98° . Find the measure of the third angle.

56°

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The measures of two angles of a triangle are 61° and 84° . Find the measure of the third angle.

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The measures of two angles of a triangle are 105° and 31° . Find the measure of the third angle.

44°

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The measures of two angles of a triangle are 47° and 72° . Find the measure of the third angle.

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One angle of a right triangle measures 33° . What is the measure of the other angle?

57°

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One angle of a right triangle measures 51° . What is the measure of the other angle?

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One angle of a right triangle measures 22.5 ° . What is the measure of the other angle?

67.5°

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One angle of a right triangle measures 36.5 ° . What is the measure of the other angle?

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The two smaller angles of a right triangle have equal measures. Find the measures of all three angles.

45°, 45°, 90°

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The measure of the smallest angle of a right triangle is 20° less than the measure of the other small angle. Find the measures of all three angles.

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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°

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The angles in a triangle are such that the measure of one angle is 20° 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.

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Find the Length of the Missing Side In the following exercises, Δ A B C is similar to Δ X Y Z . Find the length of the indicated side.

Two triangles are shown. They appear to be the same shape, but the triangle on the right is smaller. The vertices of the triangle on the left are labeled A, B, and C. The side across from A is labeled 9, the side across from B is labeled b, and the side across from C is labeled 15. The vertices of the triangle on the right are labeled X, Y, and Z. The side across from X is labeled x, the side across from Y is labeled 8, and the side across from Z is labeled 10.

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.
A triangle is shown. The vertices are labeled San Francisco, Las Vegas, and Los Angeles. The side across from San Francisco is labeled 1 inch, the side across from Las Vegas is labeled 1.3 inches, and the side across from Los Angeles is labeled 2.1 inches.

Find the distance from Los Angeles to San Francisco.

351 miles

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Find the distance from San Francisco to Las Vegas.

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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 13-foot string of lights will be attached to the top of a 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?

A vertical pole is shown with a string of lights going from the top of the pole to the ground. The pole is labeled 12 feet. The string of lights is labeled 13 feet.

5 feet

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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?

A picture of a house is shown. The rectangular garage is 12 feet high and 16 feet wide. A blue banner goes diagonally across the garage.
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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?

A square garden is shown. One side is labeled as 10 feet. There is a diagonal path of blue circular stones going from the lower left corner to the upper right corner.

14.1 feet

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Brian borrowed a 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?

A picture of a house is shown with a ladder leaning against it. The ladder is labeled 20 feet tall. The horizontal distance from the house to the base of the ladder is 6 feet.
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Everyday math

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

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Measurement A city engineer plans to build a footbridge across a lake from point X to point Y , as shown in the picture below. To find the length of the footbridge, she draws a right triangle XYZ , with right angle at X . She measures the distance from X to Z , 800 feet, and from Y to Z , 1,000 feet. How long will the bridge be?

A lake is shown. Point Y is on one side of the lake, directly across from point X. Point Z is on the same side of the lake as point X.
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Writing exercises

Write three of the properties of triangles from this section and then explain each in your own words.

Answers will vary.

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Explain how the figure below illustrates the Pythagorean Theorem for a triangle with legs of length 3 and 4 .

Three squares are shown, forming a right triangle in the center. Each square is divided into smaller squares. The smallest square is divided into 9 small squares. The medium square is divided into 16 small squares. The large square is divided into 25 small squares.
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Self check

After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

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What does this checklist tell you about your mastery of this section? What steps will you take to improve?

Questions & Answers

what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
s. Reply
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Jeannette has $5 and $10 bills in her wallet. The number of fives is three more than six times the number of tens. Let t represent the number of tens. Write an expression for the number of fives.
August Reply
What is the expressiin for seven less than four times the number of nickels
Leonardo Reply
How do i figure this problem out.
how do you translate this in Algebraic Expressions
linda Reply
why surface tension is zero at critical temperature
Shanjida
I think if critical temperature denote high temperature then a liquid stats boils that time the water stats to evaporate so some moles of h2o to up and due to high temp the bonding break they have low density so it can be a reason
s.
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
Practice Key Terms 9

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Source:  OpenStax, Prealgebra. OpenStax CNX. Jul 15, 2016 Download for free at http://legacy.cnx.org/content/col11756/1.9
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