# 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?

how can chip be made from sand
are nano particles real
yeah
Joseph
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
no can't
Lohitha
where we get a research paper on Nano chemistry....?
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
has a lot of application modern world
Kamaluddeen
yes
narayan
what is variations in raman spectra for nanomaterials
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
A soccer field is a rectangle 130 meters wide and 110 meters long. The coach asks players to run from one corner to the other corner diagonally across. What is that distance, to the nearest tenths place.
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?