What is the area of a 30-60-90 triangle?

Area = $$\frac{1}{2} \times \text{base} \times \text{height}$$ . For a 30-60-90 triangle, Area = $$\frac{1}{2} \times x \times x$$ ext{√3} $$ = $$ rac{x^2 ext{√3}}{2}@@.

What is the area of a 45-45-90 triangle?

Area = $$\frac{1}{2} \times \text{leg} \times \text{leg}$$ = $$\frac{x^2}{2}$$ .

How do you find the length of a side in a 30-60-90 triangle if you know the hypotenuse?

If the hypotenuse is c, then the shorter leg is $$\frac{c}{2}$$ and the longer leg is $$\frac{c \text{√3}}{2}$$ .

How do you find the length of a side in a 45-45-90 triangle if you know the hypotenuse?

If the hypotenuse is c, then each leg is $$\frac{c}{\text{√2}}$$ .

What is the Pythagorean theorem?

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides: $$a^2 + b^2 = c^2$$ .

What is the significance of special right triangles in geometry?

They provide specific ratios that simplify calculations in trigonometry and geometry, making it easier to solve problems involving angles and lengths.

What is the rule for a 3-60-90 triangle?

The sides are in the ratio $$x, x\text{√3}, 2x$$ .

Special Right Triangles Flashcards

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14 questions

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1.

FLASHCARD QUESTION

Front

What is a 30-60-90 triangle?

Back

2.

FLASHCARD QUESTION

Front

What is the relationship between the sides of a 30-60-90 triangle?

Back

3.

FLASHCARD QUESTION

Front

What is a 45-45-90 triangle?

Back

4.

FLASHCARD QUESTION

Front

What is the relationship between the sides of a 45-45-90 triangle?

Back

5.

FLASHCARD QUESTION

Front

What is the formula to find the hypotenuse in a 30-60-90 triangle?

Back

The hypotenuse is twice the length of the shortest side: Hypotenuse = 2x.

6.

FLASHCARD QUESTION

Front

What is the formula to find the longer leg in a 30-60-90 triangle?

Back

7.

FLASHCARD QUESTION

Front

What is the formula to find the hypotenuse in a 45-45-90 triangle?

Back

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