<< Chapter < Page Chapter >> Page >

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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°

Got questions? Get instant answers now!

Find the complement of a 38° angle.

Got questions? Get instant answers now!

Find the complement of a 27.5° angle.

62.5°

Got questions? Get instant answers now!

Find the supplement of a 109.5° angle.

Got questions? Get instant answers now!

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

62°, 118°

Got questions? Get instant answers now!
Practice Key Terms 9

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Prealgebra. OpenStax CNX. Jul 15, 2016 Download for free at http://legacy.cnx.org/content/col11756/1.9
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

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

Ask