Right Triangles and Coordinate Geometry Quiz

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.