What is a special right triangle?
Flashcard: Special Right Triangles

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•
Mathematics
•
8th - 11th Grade
•
Hard
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1.
FLASHCARD QUESTION
Front
Back
A special right triangle is a right triangle with specific angle measures and side length ratios that make calculations easier. The two main types are the 45-45-90 triangle and the 30-60-90 triangle.
2.
FLASHCARD QUESTION
Front
What are the side ratios of a 45-45-90 triangle?
Back
In a 45-45-90 triangle, the side lengths are in the ratio 1:1:√2. The legs are equal, and the hypotenuse is √2 times the length of each leg.
3.
FLASHCARD QUESTION
Front
What are the side ratios of a 30-60-90 triangle?
Back
In a 30-60-90 triangle, the side lengths are in the ratio 1:√3:2. The shortest side (opposite the 30° angle) is 1, the longer leg (opposite the 60° angle) is √3, and the hypotenuse is 2.
4.
FLASHCARD QUESTION
Front
How do you find the length of the hypotenuse in a 45-45-90 triangle if one leg is 5?
Back
If one leg is 5, the hypotenuse is 5√2, since the hypotenuse is √2 times the length of each leg.
5.
FLASHCARD QUESTION
Front
How do you find the length of the longer leg in a 30-60-90 triangle if the shorter leg is 4?
Back
If the shorter leg is 4, the longer leg is 4√3, since the longer leg is √3 times the length of the shorter leg.
6.
FLASHCARD QUESTION
Front
What is the formula to calculate the area of a right triangle?
Back
The area of a right triangle is calculated using the formula: Area = (1/2) × base × height.
7.
FLASHCARD QUESTION
Front
What is the Pythagorean theorem?
Back
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b): c² = a² + b².
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