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

A right triangle is shown. The right angle is marked with a box. The side across from the right angle is labeled as 17. One of the sides touching the right angle is labeled as 15, the other is labeled “b”.

8

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

A right triangle is shown. The right angle is marked with a box. The side across from the right angle is labeled as 15. One of the sides touching the right angle is labeled as 9, the other is labeled “b”.

12

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Kelvin is building a gazebo and wants to brace each corner by placing a 10-inch wooden bracket diagonally as shown. How far below the corner should he fasten the bracket if he wants the distances from the corner to each end of the bracket to be equal? Approximate to the nearest tenth of an inch.

A picture of a gazebo is shown. Beneath the roof is a rectangular shape. There are two braces from the top to each side. The brace on the left is labeled as 10 inches. From where the brace hits the side to the roof is labeled as x.

Solution

Step 1. Read the problem.
Step 2. Identify what you 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.
Substitute.

.
Step 5. Solve the equation.
Isolate the variable.
Use the definition of the square root.
Simplify. Approximate to the nearest tenth.
.
Step 6. Check:
.
Yes.
Step 7. Answer the question. Kelvin should fasten each piece of wood approximately 7.1" from the corner.
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John puts the base of a 13-ft ladder 5 feet from the wall of his house. How far up the wall does the ladder reach?

A picture of a house is shown. There is a ladder leaning against the side of the house. The ladder is labeled 13 feet. The horizontal distance from the ladder's base to the house is labeled 5 feet.

12 feet

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Randy wants to attach a 17-ft string of lights to the top of the 15-ft mast of his sailboat. How far from the base of the mast should he attach the end of the light string?

A picture of a boat is shown. The height of the center pole is labeled 15 feet. The string of lights is at a diagonal from the top of the pole and is labeled 17 feet.

8 feet

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Key concepts

  • Supplementary and Complementary Angles
    • If the sum of the measures of two angles is 180°, then the angles are supplementary.
    • If A and B are supplementary, then m A + m B = 180 .
    • If the sum of the measures of two angles is 90°, then the angles are complementary.
    • If A and B are complementary, then m A + m B = 90 .
  • Solve Geometry Applications
    1. Read the problem and make sure you understand all the words and ideas. Draw a figure and label it with the given information.
    2. Identify what you are looking for.
    3. Name what you are looking for and choose a variable to represent it.
    4. Translate into an equation by writing the appropriate formula or model for the situation. Substitute in the given information.
    5. Solve the equation using good algebra techniques.
    6. Check the answer in the problem and make sure it makes sense.
    7. Answer the question with a complete sentence.
  • Sum of the Measures of the Angles of a Triangle

    ..

    • For any Δ A B C , the sum of the measures is 180°
    • m A + m B = 180
  • Right Triangle

    .

    • A right triangle is a triangle that has one 90° angle, which is often marked with a symbol.
  • Properties of Similar Triangles
    • If two triangles are similar, then their corresponding angle measures are equal and their corresponding side lengths have the same ratio.

Practice makes perfect

Use the Properties of Angles

In the following exercises, find the supplement and the complement of the given angle.

In the following exercises, use the properties of angles to solve.

Find the supplement of a 135° angle.

45°

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Find the complement of a 38° angle.

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Find the complement of a 27.5° angle.

62.5°

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Find the supplement of a 109.5° angle.

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Two angles are supplementary. The larger angle is 56° more than the smaller angle. Find the measures of both angles.

62°, 118°

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Questions & Answers

current economic plans (MDGS) needs
Ajijola Reply
I don't know what is happening
surajkumar
What is economic
Joeali Reply
What is the importance of study economics
Wilma
Economic is the study of how humans make decisions in face of sacristy
Wilma
economics is the study of how humans makes decision in the face of scarcity
Kpienta
economics is the study of human behaviour when faced with difficult situation example when goods and services are scarcity.
Sydney
what is Economic
Dauda Reply
what is 4ps of economic?
thomas Reply
production place Price product
Benedict
Criticism of elasticity
Siddikur Reply
what is unemployment
Gyamfi Reply
ohk thanks
Gyamfi
why is unemployment rapid in the country
Gyamfi
I need more explanation
Odo
what is unemployment
Munanag Reply
not working
Bethel
some one who is willing qualified to work but can't find job
jackie
Bethel...explain? please
Abubakar
some one who is willing to work but can't find job
Hawa
Yes true
Brian
which one please
Hawa
unemployment refers to the ability for someone who is capable and willing to work but could not find a job..
Mnoko
some one who not able to find a job
Dennis
please what is the secret of learning?
thomas
What is stock market?
JOHN Reply
explain the various types of cost curve
Ruth Reply
Short-run average fixed cost (SRAFC) Short-run average total cost (SRAC or SRATC) Short-run average variable cost (AVC or SRAVC) Short-run fixed cost (FC or SRFC) Short-run marginal cost (SRMC) Short-run total cost (SRTC)
Romy
what's economic development and growth
Popoola Reply
what do you understand by Ceteris Paribus?
Gabriel Reply
the external factor will remained constant, except the price
Hasib
everything being equal
Chenwi
explain the uses of microeconomics
Nikita Reply
uses of microeconomics
Nikita
Adam Smith's definition of economics
Sylvia Reply
what is economic deficit
Amjad
this is a situation whereby a nation's outcome or available resources are not enough to the people thereby causing scarcity
Ariel
prices of Quality demanded is equal to Quality supplied
NABUBOLO Reply
it's quantity demand and quantity supplied that's called equilibrium
Romy
no
NABUBOLO
they deal With prices
NABUBOLO
define the elasticity
NABUBOLO
explain different types of elasticity
NABUBOLO
oops 😬 you are right you talk about quality I tell about quantity
Romy
elasticity is the measurement of the percentage change of one economic variable in response to a change in another
Romy
Cross Elasticity of Demand (XED) Income Elasticity of Demand (YED) Price Elasticity of Supply (PES)
Romy
anything else?
Romy
I need to know everything about theory of consumer behavior
Grace
Romy, what is microeconomic?
thomas
What is Economic please
Dauda
Thomas, microeconomics is the study of how consumers, workers, and firms interact to generate outcomes in specific markets
Kieran
Dauda, economics is the study of people and choices. it is on one side the study of wealth and on the more important side, a part of the study if man
Kieran
How does one analyze a market where both demand and supply shift?
Gabriel Reply
That's equilibrium market
Ramon
but an equlibrum can appear twice on the same market... both in Movement along the Demand/supply curve of shift in the Curve
Gabriel
I Mean on the same curve..
Gabriel
how can consumer surplus be calculated
Franklyn
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.
Kimberly Reply
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.
August Reply
What is the expressiin for seven less than four times the number of nickels
Leonardo Reply
How do i figure this problem out.
how do you translate this in Algebraic Expressions
linda Reply
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)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
Practice Key Terms 9

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Source:  OpenStax, Prealgebra. OpenStax CNX. Jul 15, 2016 Download for free at http://legacy.cnx.org/content/col11756/1.9
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