<< Chapter < Page Chapter >> Page >

Because the Pythagorean Theorem contains variables that are squared, to solve for the length of a side in a right triangle, we will have to use square roots.

Use the Pythagorean Theorem to find the length of the hypotenuse shown below.

A right triangle with legs marked 3 and 4.

Solution

Step 1. Read the problem.
Step 2. Identify what you are looking for. the length of the hypotenuse of the triangle
Step 3. Name. Choose a variable to represent it.
Label side c on the figure.
Let c = the length of the hypotenuse.

.
Step 4. Translate.
Write the appropriate formula. a 2 + b 2 = c 2
Substitute. 3 2 + 4 2 = c 2
Step 5. Solve the equation. 9 + 16 = c 2
Simplify. 25 = c 2
Use the definition of square root. 25 = c
Simplify. 5 = c
Step 6. Check.

.
Step 7. Answer the question. The length of the hypotenuse is 5.

Got questions? Get instant answers now!
Got questions? Get instant answers now!

Use the Pythagorean Theorem to find the length of the hypotenuse in the triangle shown below.

A right triangle with legs marked 6 and 8. The hypotenuse is marked c.

c = 10

Got questions? Get instant answers now!

Use the Pythagorean Theorem to find the length of the hypotenuse in the triangle shown below.

No Alt Text

c = 13

Got questions? Get instant answers now!

Use the Pythagorean Theorem to find the length of the leg shown below.

A right angle with one leg marked 5. The hypotenuse is labeled 13.

Solution

Step 1. Read the problem.
Step 2. Identify what you are looking for. the length of the leg of the triangle
Step 3. Name. Choose a variable to represent it. Let b = the leg of the triangle.
Lable side b . .
Step 4. Translate
Write the appropriate formula. a 2 + b 2 = c 2
Substitute. 5 2 + b 2 = 13 2
Step 5. Solve the equation. 25 + b 2 = 169
Isolate the variable term. b 2 = 144
Use the definition of square root. b 2 = 144
Simplify. b = 12
Step 6. Check.

.
Step 7. Answer the question. The length of the leg is 12.

Got questions? Get instant answers now!
Got questions? Get instant answers now!

Use the Pythagorean Theorem to find the length of the leg in the triangle shown below.

A right triangle with legs marked b and 15. The hypotenuse is marked 17.

8

Got questions? Get instant answers now!

Use the Pythagorean Theorem to find the length of the leg in the triangle shown below.

A right triangle with legs marked b and 9. The hypotenuse is marked 15.

12

Got questions? Get instant answers now!
A gazebo is shown. In one of its corners, a triangle is made with the wood. The hypotenuse is marked 10 inches, and one of the legs is marked x

Kelvin is building a gazebo and wants to brace each corner by placing a 10 piece of wood diagonally as shown above.

If he fastens the wood so that the ends of the brace are the same distance from the corner, what is the length of the legs of the right triangle formed? Approximate to the nearest tenth of an inch.

Solution

Step 1. Read the problem. Step 2. Identify what we are looking for. the distance from the corner that the bracket should be attached Step 3. Name. Choose a variable to represent it. Let x = the distance from the corner. Step 4. Translate. Write the appropriate formula and substitute. Step 5. Solve the equation. Isolate the variable. Use the definition of square root. Simplify. Approximate to the nearest tenth. a 2 + b 2 = c 2 x 2 + x 2 = 10 2 2 x 2 = 100 x 2 = 50 x = 50 x 7.1 Step 6. Check. a 2 + b 2 = c 2 ( 7.1 ) 2 + ( 7.1 ) 2 10 2 Yes. Step 7. Answer the question. Kelvin should fasten each piece of wood approximately 7.1 from the corner.

Got questions? Get instant answers now!
Got questions? Get instant answers now!

John puts the base of a 13-foot ladder five feet from the wall of his house as shown below. How far up the wall does the ladder reach?

A house is shown with a ladder leaning against it. The ladder is marked 13’, and the distance from the house to the base of the ladder is marked 5’.

12 feet

Got questions? Get instant answers now!

Randy wants to attach a 17 foot string of lights to the top of the 15 foot mast of his sailboat, as shown below. How far from the base of the mast should he attach the end of the light string?

A sailboat is shown with a 15’ mast (the straight tall part). From the top of the mast, a series of colored dots stretches down to the back of the boat and is marked 17’.

8 feet

Got questions? Get instant answers now!

Solve applications using rectangle properties

You may already be familiar with the properties of rectangles. Rectangles have four sides and four right ( 90 ° ) angles. The opposite sides of a rectangle are the same length. We refer to one side of the rectangle as the length, L , and its adjacent side as the width, W .

Questions & Answers

what is mutation
Janga Reply
what is a cell
Sifune Reply
how is urine form
Sifune
what is antagonism?
mahase Reply
classification of plants, gymnosperm features.
Linsy Reply
what is the features of gymnosperm
Linsy
how many types of solid did we have
Samuel Reply
what is an ionic bond
Samuel
What is Atoms
Daprince Reply
what is fallopian tube
Merolyn
what is bladder
Merolyn
what's bulbourethral gland
Eduek Reply
urine is formed in the nephron of the renal medulla in the kidney. It starts from filtration, then selective reabsorption and finally secretion
onuoha Reply
State the evolution relation and relevance between endoplasmic reticulum and cytoskeleton as it relates to cell.
Jeremiah
what is heart
Konadu Reply
how is urine formed in human
Konadu
how is urine formed in human
Rahma
what is the diference between a cavity and a canal
Pelagie Reply
what is the causative agent of malaria
Diamond
malaria is caused by an insect called mosquito.
Naomi
Malaria is cause by female anopheles mosquito
Isaac
Malaria is caused by plasmodium Female anopheles mosquitoe is d carrier
Olalekan
a canal is more needed in a root but a cavity is a bad effect
Commander
what are pathogens
Don Reply
In biology, a pathogen (Greek: πάθος pathos "suffering", "passion" and -γενής -genēs "producer of") in the oldest and broadest sense, is anything that can produce disease. A pathogen may also be referred to as an infectious agent, or simply a germ. The term pathogen came into use in the 1880s.[1][2
Zainab
A virus
Commander
Definition of respiration
Muhsin Reply
respiration is the process in which we breath in oxygen and breath out carbon dioxide
Achor
how are lungs work
Commander
where does digestion begins
Achiri Reply
in the mouth
EZEKIEL
what are the functions of follicle stimulating harmones?
Rashima Reply
stimulates the follicle to release the mature ovum into the oviduct
Davonte
what are the functions of Endocrine and pituitary gland
Chinaza
endocrine secrete hormone and regulate body process
Achor
while pituitary gland is an example of endocrine system and it's found in the Brain
Achor
what's biology?
Egbodo Reply
Biology is the study of living organisms, divided into many specialized field that cover their morphology, physiology,anatomy, behaviour,origin and distribution.
Lisah
biology is the study of life.
Alfreda
Biology is the study of how living organisms live and survive in a specific environment
Sifune
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Elementary algebra. OpenStax CNX. Jan 18, 2017 Download for free at http://cnx.org/content/col12116/1.2
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Elementary algebra' conversation and receive update notifications?

Ask