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Algebraic

For the following exercises, use cofunctions of complementary angles.

cos ( 34° ) = sin ( __° )

cos ( π 3 ) = sin (___)

π 6

csc ( 21° ) = sec ( ___° )

tan ( π 4 ) = cot ( __ )

π 4

For the following exercises, find the lengths of the missing sides if side a is opposite angle A , side b is opposite angle B , and side c is the hypotenuse.

cos B = 4 5 , a = 10

sin B = 1 2 ,   a = 20

b = 20 3 3 , c = 40 3 3

tan A = 5 12 , b = 6

tan A = 100 , b = 100

a = 10 , 000 , c = 10 , 000.5

sin B = 1 3 ,   a = 2

a = 5 , A = 60

b = 5 3 3 , c = 10 3 3

c = 12 , A = 45

Graphical

For the following exercises, use [link] to evaluate each trigonometric function of angle A .

A right triangle with sides 4 and 10 and angle of A labeled.

sin A

5 29 29

cos A

tan A

5 2

csc A

sec A

29 2

cot A

For the following exercises, use [link] to evaluate each trigonometric function of angle A .

A right triangle with sides of 10 and 8 and angle of A labeled.

sin A

5 41 41

cos A

tan A

5 4

csc A

sec A

41 4

cot A

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

A right triangle with sides of 7, b, and c labeled. Angles of B and 30 degrees also labeled.

c = 14 ,   b = 7 3

A right triangle with sides of 10, a, and c. Angles of 60 degrees and A also labeled.
A right triangle with corners labeled A, B, and C. Hypotenuse has length of 15 times square root of 2. Angle B is 45 degrees.

a = 15 ,   b = 15

Technology

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

A right triangle with sides of 10, a, and c. Angles of A and 62 degrees are also labeled.
A right triangle with sides of 7, b, and c. Angles of 35 degrees and B are also labeled.

b = 9.9970 ,   c = 12.2041

A right triangle with sides of a, b, and 10 labeled. Angles of 65 degrees and B are also labeled.
A right triangle with sides a, b, and 12. Angles of 10 degrees and B are also labeled.

a = 2.0838 ,   b = 11.8177

A right triangle with corners labeled A, B, and C. Sides labeled b, c, and 16.5. Angle of 81 degrees also labeled.

b = 15 , B = 15

a = 55.9808 , c = 57.9555

c = 200 , B = 5

c = 50 , B = 21

a = 46.6790 , b = 17.9184

a = 30 , A = 27

b = 3.5 , A = 78

a = 16.4662 , c = 16.8341

Extensions

Find x .

A triangle with angles of 63 degrees and 39 degrees and side x. Bisector in triangle with length of 82.

Find x .

A triangle with angles of 36 degrees and 50 degrees and side x. Bisector in triangle with length of 85.

188.3159

Find x .

A right triangle with side of 115 and angle of 35 degrees. Within right triangle there is another right triangle with angle of 56 degrees. Side length difference between two triangles is x.

Find x .

A right triangle with side of 119 and angle of 26 degrees. Within right triangle there is another right triangle with angle of 70 degrees instead of 26 degrees. Difference in side length between two triangles is 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 36° , and that the angle of depression to the bottom of the tower is 23° . 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 43° , and that the angle of depression to the bottom of the tower is 31° . 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 15° , and that the angle of depression to the bottom of the tower is . 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 18° , and that the angle of depression to the bottom of the tower is . 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 40° . From the same location, the angle of elevation to the top of the antenna is measured to be 43° . 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 36° . From the same location, the angle of elevation to the top of the lightning rod is measured to be 38° . 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 80° . How high does the ladder reach up the side of the building?  

Questions & Answers

anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
Introduction about quantum dots in nanotechnology
Praveena Reply
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
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
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
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
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
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Contemporary math applications. OpenStax CNX. Dec 15, 2014 Download for free at http://legacy.cnx.org/content/col11559/1.6
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