University:
Felician University
Course:
MATH-231 | Geometry I
Academic year:

2019
Views:

62

Pages:

4
Author:

larbiwxcvbn

Right Triangles Special Triangles (45-45-90 & 30-60-90) Pythagorean Theorem The Pythagorean Theorem: a² + b² = c² Special Triangle: 45°-45°-90° Special Triangle: 30°-60°-90° Pythagorean Triples There are infinitely many Pythagorean triples, but here are some that are commonly used: 3, 4, 5 5, 12, 13 8, 15, 17 7, 24, 25 Use the Pythagorean Theorem, if applicable, to find the missing side. Converse of the Pythagorean Theorem Right Triangle: a² + b² = c² Acute Triangle: c² < a² + b² Obtuse Triangle: c² > a² + b² Are these triangles RIGHT, ACUTE, OBTUSE, or NOT a TRIANGLE? 1. 3, 4, 5: RIGHT TRIANGLE 2. 5, 8, 9: ACUTE 3. 6, 8, 11: OBTUSE 4. 11, 15, 18: NOT A TRIANGLE 5. 5, 12, 13: RIGHT TRIANGLE 6. 3, 8, 10: OBTUSE A person is standing 20 feet from a flagpole. If the angle of elevation to the top of the flagpole is 72°, what is the length of the flagpole? x² + 20² = x² + 400 = 15.02 m A ladder is placed 5 feet from the base of a wall. If the ladder reaches 11 feet up the wall, how long is the ladder? 8² + 11² = x² 64 + 121 = x² x = √185 = 13.6 ft Special Triangles (45°-45°-90°) AKA: Isosceles Right Triangle Special Triangles (30°-60°-90°) AKA: Not an Isosceles Right Triangle Find the missing side. Rationalize denominators if applicable. * √(5² + 5²) = 5√2 * √(3² + 3²) = 3√2 * √(1² + 1²) = √2 * √(5² + 5²) = 5√2 * √(3² + 3²) = 3√2 * √(1² + 1²) = √2 Find the missing side. Rationalize denominators if applicable. * √(3² + 3²) = 3√2 * √(4² + 4²) = 4√2 * √(5² + 5²) = 5√2 * √(3² + 3²) = 3√2 * √(4² + 4²) = 4√2 * √(5² + 5²) = 5√2