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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

how can chip be made from sand
Eke Reply
is this allso about nanoscale material
Almas
are nano particles real
Missy Reply
yeah
Joseph
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
Lale Reply
no can't
Lohitha
where is the latest information on a no technology how can I find it
William
currently
William
where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
Maira Reply
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
Google
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
Hafiz Reply
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
Jyoti Reply
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
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
Brian Reply
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?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
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 ?
Bob Reply
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
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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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