Given a right triangle with side lengths = cm, = cm, and = cm, what is the perimeter of the triangle?
Table of contents
- 0. Review of College Algebra4h 43m
- 1. Measuring Angles40m
- 2. Trigonometric Functions on Right Triangles2h 5m
- 3. Unit Circle1h 19m
- 4. Graphing Trigonometric Functions1h 19m
- 5. Inverse Trigonometric Functions and Basic Trigonometric Equations1h 41m
- 6. Trigonometric Identities and More Equations2h 34m
- 7. Non-Right Triangles1h 38m
- 8. Vectors2h 25m
- 9. Polar Equations2h 5m
- 10. Parametric Equations1h 6m
- 11. Graphing Complex Numbers1h 7m
- OLD 1. Angles and the Trigonometric Functions Coming soon
- OLD 2. Trigonometric Functions graphs, Inverse Trigonometric Functions Coming soon
- OLD 3. Trigonometric Identities and Equations Coming soon
- OLD 4. Laws of Sines, Cosines and Vectors Coming soon
- OLD 5. Complex Numbers, Polar Coordinates and Parametric Equations Coming soon
- NEW (not used) 7. Laws of Sines, Cosines and Vectors Coming soon
- NEW (not used) 8. Vectors Coming soon
- NEW(not used) 9. Polar equations Coming soon
- NEW (not used) 11. Graphing Complex Numbers Coming soon
0. Review of College Algebra
Pythagorean Theorem & Basics of Triangles
Multiple Choice
A ladder is leaning against a wall. The foot of the ladder is meters away from the wall, and the ladder reaches a height of meters on the wall. What is the length of the ladder?
A
meters
B
meters
C
meters
D
meters
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Verified step by step guidance1
Identify the right triangle formed by the ladder, the wall, and the ground. The ladder acts as the hypotenuse, the distance from the wall is one leg, and the height the ladder reaches on the wall is the other leg.
Label the sides: let the distance from the wall be \(a = 6\) meters, the height on the wall be \(b = 8\) meters, and the length of the ladder (hypotenuse) be \(c\) meters.
Recall the Pythagorean theorem for right triangles: \(c^2 = a^2 + b^2\).
Substitute the known values into the equation: \(c^2 = 6^2 + 8^2\).
Calculate the squares and sum them: \(c^2 = 36 + 64\), then find \(c\) by taking the square root of the sum, i.e., \(c = \sqrt{36 + 64}\).
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