Podcast
Questions and Answers
What do special right triangles refer to?
What do special right triangles refer to?
- Triangles with obtuse angles
- 45-45-90 and 30-60-90 triangles (correct)
- Triangles with equal sides
- Isosceles triangles
How do you find the hypotenuse in a 45-45-90 triangle?
How do you find the hypotenuse in a 45-45-90 triangle?
hypotenuse = leg x √2
How do you find the hypotenuse in a 30-60-90 triangle?
How do you find the hypotenuse in a 30-60-90 triangle?
hypotenuse = shortest leg x 2
How do you find the longest leg of a 30-60-90 triangle?
How do you find the longest leg of a 30-60-90 triangle?
What is Theorem 9.8 (45-45-90 Theorem)?
What is Theorem 9.8 (45-45-90 Theorem)?
What is Theorem 9.9 (30-60-90 Theorem)?
What is Theorem 9.9 (30-60-90 Theorem)?
What are trigonometric ratios?
What are trigonometric ratios?
What does SOHCAHTOA stand for?
What does SOHCAHTOA stand for?
What does it mean to solve a right triangle?
What does it mean to solve a right triangle?
Study Notes
Special Right Triangles
- Includes two types of triangles: 45-45-90 and 30-60-90.
- Known for consistent relationships among their side lengths.
45-45-90 Triangle
- Hypotenuse can be calculated using the formula: hypotenuse = leg x √2.
30-60-90 Triangle
- Hypotenuse is found using: hypotenuse = shortest leg x 2.
- The longest leg (2nd longest side) can be determined as: longest leg = shortest leg x √3.
Theorems
- Theorem 9.8 (45-45-90 Theorem): In this triangle, the hypotenuse measures √2 times the length of each leg.
- Theorem 9.9 (30-60-90 Theorem): In this triangle, the hypotenuse is twice the length of the shortest leg, while the longer leg equals √3 times the shortest leg.
Trigonometric Ratios
- Essential for calculating side lengths in right triangles.
SOHCAHTOA
- A mnemonic to remember trigonometric functions:
- SIN (sine): Opposite/Hypotenuse
- COS (cosine): Adjacent/Hypotenuse
- TAN (tangent): Opposite/Adjacent
Solving a Right Triangle
- Involves calculating all six measurements: three side lengths and three angle measures.
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Description
Test your knowledge on special right triangles with this quiz. Explore the relationships between side lengths in 45-45-90 and 30-60-90 triangles. Learn how to find the hypotenuse and longest leg with ease.
