# 9.3 Use properties of angles, triangles, and the pythagorean theorem  (Page 6/15)

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Two angles are supplementary. The smaller angle is $\text{36°}$ less than the larger angle. Find the measures of both angles.

Two angles are complementary. The smaller angle is $\text{34°}$ less than the larger angle. Find the measures of both angles.

62°, 28°

Two angles are complementary. The larger angle is $\text{52°}$ 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 $\text{26°}$ and $\text{98°}.$ Find the measure of the third angle.

56°

The measures of two angles of a triangle are $\text{61°}$ and $\text{84°}.$ Find the measure of the third angle.

The measures of two angles of a triangle are $\text{105°}$ and $\text{31°}.$ Find the measure of the third angle.

44°

The measures of two angles of a triangle are $\text{47°}$ and $\text{72°}.$ Find the measure of the third angle.

One angle of a right triangle measures $\text{33°}.$ What is the measure of the other angle?

57°

One angle of a right triangle measures $\text{51°}.$ What is the measure of the other angle?

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

67.5°

One angle of a right triangle measures $36.5°.$ 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 $\text{20°}$ 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 $\text{20°}$ 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, $\text{Δ}ABC$ is similar to $\text{Δ}XYZ.$ Find the length of the indicated side.

side $b$

12

side $x$

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.

15

25

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.

8

12

10.2

8

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?

## 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

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 $\text{Z},1,000$ feet. How long will the bridge be?

## Writing exercises

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

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

## Self check

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?

what does nano mean?
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?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
what is fullerene does it is used to make bukky balls
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
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?
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 ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
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
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
types of nano material
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.
what is nano technology
what is system testing?
preparation of nanomaterial
how did you get the value of 2000N.What calculations are needed to arrive at it
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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.
What is the expressiin for seven less than four times the number of nickels
How do i figure this problem out.
how do you translate this in Algebraic Expressions
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)=
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?