# 5.2 Right triangle trigonometry  (Page 6/12)

 Page 6 / 12

## Algebraic

For the following exercises, use cofunctions of complementary angles.

$\mathrm{cos}\left(\text{34°}\right)=\mathrm{sin}\left(\text{__°}\right)$

$\mathrm{cos}\left(\frac{\pi }{3}\right)=\mathrm{sin}\text{(___)}$

$\frac{\pi }{6}$

$\mathrm{csc}\left(\text{21°}\right)=\mathrm{sec}\left(\text{___°}\right)$

$\mathrm{tan}\left(\frac{\pi }{4}\right)=\mathrm{cot}\left(\text{__}\right)$

$\frac{\pi }{4}$

For the following exercises, find the lengths of the missing sides if side $\text{\hspace{0.17em}}a\text{\hspace{0.17em}}$ is opposite angle $\text{\hspace{0.17em}}A,$ side $\text{\hspace{0.17em}}b\text{\hspace{0.17em}}$ is opposite angle $\text{\hspace{0.17em}}B,$ and side $\text{\hspace{0.17em}}c\text{\hspace{0.17em}}$ is the hypotenuse.

$\mathrm{cos}\text{\hspace{0.17em}}B=\frac{4}{5},a=10$

$b=\frac{20\sqrt{3}}{3},c=\frac{40\sqrt{3}}{3}$

$\mathrm{tan}\text{\hspace{0.17em}}A=\frac{5}{12},b=6$

$\mathrm{tan}\text{\hspace{0.17em}}A=100,b=100$

$a=10,000,c=10,000.5$

$a=5,\text{\hspace{0.17em}}\measuredangle \text{\hspace{0.17em}}A={60}^{\circ }$

$b=\frac{5\sqrt{3}}{3},c=\frac{10\sqrt{3}}{3}$

$c=12,\text{\hspace{0.17em}}\measuredangle \text{\hspace{0.17em}}A={45}^{\circ }$

## Graphical

For the following exercises, use [link] to evaluate each trigonometric function of angle $\text{\hspace{0.17em}}A.$

$\mathrm{sin}\text{\hspace{0.17em}}A$

$\frac{5\sqrt{29}}{29}$

$\mathrm{cos}\text{\hspace{0.17em}}A$

$\mathrm{tan}\text{\hspace{0.17em}}A$

$\frac{5}{2}$

$\mathrm{csc}\text{\hspace{0.17em}}A$

$\mathrm{sec}\text{\hspace{0.17em}}A$

$\frac{\sqrt{29}}{2}$

$\mathrm{cot}\text{\hspace{0.17em}}A$

For the following exercises, use [link] to evaluate each trigonometric function of angle $\text{\hspace{0.17em}}A.$

$\mathrm{sin}\text{\hspace{0.17em}}A$

$\frac{5\sqrt{41}}{41}$

$\mathrm{cos}\text{\hspace{0.17em}}A$

$\mathrm{tan}\text{\hspace{0.17em}}A$

$\frac{5}{4}$

$\mathrm{csc}\text{\hspace{0.17em}}A$

$\mathrm{sec}\text{\hspace{0.17em}}A$

$\frac{\sqrt{41}}{4}$

$\mathrm{cot}\text{\hspace{0.17em}}A$

For the following exercises, solve for the unknown sides of the given triangle.

## Technology

For the following exercises, use a calculator to find the length of each side to four decimal places.

$b=15,\text{\hspace{0.17em}}\measuredangle B={15}^{\circ }$

$a=55.9808,c=57.9555$

$c=200,\text{\hspace{0.17em}}\measuredangle B={5}^{\circ }$

$c=50,\text{\hspace{0.17em}}\measuredangle B={21}^{\circ }$

$a=46.6790,b=17.9184$

$a=30,\text{\hspace{0.17em}}\measuredangle A={27}^{\circ }$

$b=3.5,\text{\hspace{0.17em}}\measuredangle A={78}^{\circ }$

$a=16.4662,c=16.8341$

## Extensions

Find $\text{\hspace{0.17em}}x.$

Find $\text{\hspace{0.17em}}x.$

188.3159

Find $\text{\hspace{0.17em}}x.$

Find $\text{\hspace{0.17em}}x.$

200.6737

A radio tower is located 400 feet from a building. From a window in the building, a person determines that the angle of elevation to the top of the tower is $\text{\hspace{0.17em}}36°,$ and that the angle of depression to the bottom of the tower is $\text{\hspace{0.17em}}23°.\text{\hspace{0.17em}}$ How tall is the tower?

A radio tower is located 325 feet from a building. From a window in the building, a person determines that the angle of elevation to the top of the tower is $\text{\hspace{0.17em}}43°,$ and that the angle of depression to the bottom of the tower is $\text{\hspace{0.17em}}31°.\text{\hspace{0.17em}}$ How tall is the tower?

498.3471 ft

A 200-foot tall monument is located in the distance. From a window in a building, a person determines that the angle of elevation to the top of the monument is $\text{\hspace{0.17em}}15°,$ and that the angle of depression to the bottom of the tower is $\text{\hspace{0.17em}}2°.\text{\hspace{0.17em}}$ How far is the person from the monument?

A 400-foot tall monument is located in the distance. From a window in a building, a person determines that the angle of elevation to the top of the monument is $\text{\hspace{0.17em}}18°,$ and that the angle of depression to the bottom of the tower is $\text{\hspace{0.17em}}3°.\text{\hspace{0.17em}}$ How far is the person from the monument?

1060.09 ft

There is an antenna on the top of a building. From a location 300 feet from the base of the building, the angle of elevation to the top of the building is measured to be $\text{\hspace{0.17em}}40°.\text{\hspace{0.17em}}$ From the same location, the angle of elevation to the top of the antenna is measured to be $\text{\hspace{0.17em}}43°.\text{\hspace{0.17em}}$ Find the height of the antenna.

There is lightning rod on the top of a building. From a location 500 feet from the base of the building, the angle of elevation to the top of the building is measured to be $\text{\hspace{0.17em}}36°.\text{\hspace{0.17em}}$ From the same location, the angle of elevation to the top of the lightning rod is measured to be $\text{\hspace{0.17em}}38°.\text{\hspace{0.17em}}$ Find the height of the lightning rod.

27.372 ft

## Real-world applications

A 33-ft ladder leans against a building so that the angle between the ground and the ladder is $\text{\hspace{0.17em}}80°.\text{\hspace{0.17em}}$ How high does the ladder reach up the side of the building?

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
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
how did you get the value of 2000N.What calculations are needed to arrive at it
Privacy Information Security Software Version 1.1a
Good
Got questions? Join the online conversation and get instant answers!