What is the value of $$\text{√}2$$ approximately?

$$\text{√}2$$ is approximately 1.414.

If the hypotenuse of a 30-60-90 triangle is 10, what is the length of the shorter leg?

The shorter leg is $$\frac{10}{2} = 5$$ .

What is the value of $$\text{√}3$$ approximately?

$$\text{√}3$$ is approximately 1.732.

In a 45-45-90 triangle, if the hypotenuse is 8, what is the length of each leg?

Each leg is $$\frac{8}{\text{√}2} = 4\text{√}2$$ .

What is the Pythagorean theorem?

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b): $$c^2 = a^2 + b^2$$ .

If one leg of a 30-60-90 triangle is 6, what is the length of the hypotenuse?

The hypotenuse is 12, since it is twice the length of the shorter leg.

What is the length of the longer leg in a 30-60-90 triangle if the shorter leg is 3?

The longer leg is $$3\text{√}3$$ .

How do you derive the lengths of the sides in a 30-60-90 triangle?

Start with the shortest leg (opposite 30°) as $$x$$ . The longer leg (opposite 60°) is $$x\text{√}3$$ and the hypotenuse is $$2x$$ .

What is the significance of special right triangles in geometry?

Special right triangles provide specific ratios and relationships that simplify calculations in trigonometry and geometry.

Special Right Triangles Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is a 45-45-90 triangle?

Back

Tags

CCSS.8.G.B.8

2.

FLASHCARD QUESTION

Front

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

Back

Tags

CCSS.HSG.CO.C.10

3.

FLASHCARD QUESTION

Front

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

Back

Tags

CCSS.8.G.B.8

4.

FLASHCARD QUESTION

Front

How do you find the length of the longer leg in a 30-60-90 triangle?

Back

Tags

CCSS.HSG.CO.C.10

5.

FLASHCARD QUESTION

Front

What is the formula to find the area of a right triangle?

Back

Tags

CCSS.6.G.A.1

6.

FLASHCARD QUESTION

Front

If the legs of a 45-45-90 triangle are each 4, what is the length of the hypotenuse?

Back

Tags

CCSS.8.G.B.7

7.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.8.NS.A.2

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