Podcast
Questions and Answers
Which of the following sets of measures can be the sides of a right triangle?
Which of the following sets of measures can be the sides of a right triangle?
Do the coordinates A(4,6), B(9,1), and U(1,3) form a right triangle?
Do the coordinates A(4,6), B(9,1), and U(1,3) form a right triangle?
What is the missing side in the right triangle with sides 8 and 9?
What is the missing side in the right triangle with sides 8 and 9?
What is the length of the diagonal of a square with side length 7?
What is the length of the diagonal of a square with side length 7?
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A ladder leaning against a house reaches a second-story window that is 15 feet high. If the ladder is 24 feet long, how far is the base of the ladder from the bottom of the house?
A ladder leaning against a house reaches a second-story window that is 15 feet high. If the ladder is 24 feet long, how far is the base of the ladder from the bottom of the house?
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Which set of measures can be the sides of a right triangle?
Which set of measures can be the sides of a right triangle?
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Do the coordinates A(4,6), B(9,1), and U(1,3) form a right triangle?
Do the coordinates A(4,6), B(9,1), and U(1,3) form a right triangle?
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What is the length of the diagonal of a square with side length 7?
What is the length of the diagonal of a square with side length 7?
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A ladder leaning against a house reaches a second-story window that is 15 feet high. If the ladder is 24 feet long, how far is the base of the ladder from the bottom of the house?
A ladder leaning against a house reaches a second-story window that is 15 feet high. If the ladder is 24 feet long, how far is the base of the ladder from the bottom of the house?
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The angle of elevation from point A to the top of a hill is 49 degrees. If point A is 400 feet from the base of the hill, how high is the hill?
The angle of elevation from point A to the top of a hill is 49 degrees. If point A is 400 feet from the base of the hill, how high is the hill?
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Study Notes
Right Triangles
- The set of measures that can be the sides of a right triangle can be determined using the Pythagorean theorem.
Triangle with Coordinates A, B, and U
- The coordinates A(4,6), B(9,1), and U(1,3) form a right triangle if the Pythagorean theorem is satisfied.
Missing Side of a Right Triangle
- In a right triangle with sides 8 and 9, the missing side can be found using the Pythagorean theorem: √(8² + 9²) = √(64 + 81) = √145.
Diagonal of a Square
- The length of the diagonal of a square with side length 7 can be found using the Pythagorean theorem: √(7² + 7²) = √(49 + 49) = √98.
Ladder Against a House
- If a ladder leaning against a house reaches a second-story window that is 15 feet high, and the ladder is 24 feet long, the base of the ladder from the bottom of the house can be found using the Pythagorean theorem: √(24² - 15²) = √(576 - 225) = √351.
Angle of Elevation
- If the angle of elevation from point A to the top of a hill is 49 degrees, and point A is 400 feet from the base of the hill, the height of the hill can be found using trigonometry: height = 400 × tan(49) = 400 × 1.15 = 460 feet.
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Description
Test your knowledge of right triangles and coordinate geometry with this cumulative review quiz. Determine if sets of measures can be the sides of a right triangle, and find the value of missing sides using the Distance and Pythagorean Theorem. Can you determine if given coordinates form a right triangle? Put your geometry skills to the test!
