What is the formula for the area of a right triangle?

The area of a right triangle is given by the formula: $$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$$ .

How do you apply the Pythagorean theorem in special right triangles?

In special right triangles, you can use the Pythagorean theorem to verify the relationships between the sides, such as $$a^2 + b^2 = c^2$$ .

What is the value of the hypotenuse in a 30-60-90 triangle if the shorter leg is 5?

The hypotenuse is $$5 \times 2 = 10$$ .

If the hypotenuse of a 45-45-90 triangle is 10, what is the length of each leg?

Each leg is $$\frac{10}{\text{√2}} = 5\text{√2}$$ .

What is the relationship between the angles in a right triangle?

In a right triangle, the sum of the angles is always 180 degrees, with one angle being 90 degrees.

How can you determine if a triangle is a special right triangle?

A triangle is a special right triangle if it has angles of 45-45-90 or 30-60-90.

What is the significance of special right triangles in geometry?

Special right triangles simplify calculations involving angles and side lengths, making them essential in trigonometry and geometry.

How do you solve for a missing side in a special right triangle?

Use the known side lengths and the properties of special right triangles to find the missing side using ratios or the Pythagorean theorem.

Special Right Triangles Flashcards

Student preview

15 questions

Show all answers

1.

FLASHCARD QUESTION

Front

What is a special right triangle?

Back

A special right triangle is a right triangle with specific angle measures and side length ratios. The two main types are the 45-45-90 triangle and the 30-60-90 triangle.

Tags

CCSS.HSG.CO.C.10

2.

FLASHCARD QUESTION

Front

What are the side ratios of a 45-45-90 triangle?

Back

Tags

CCSS.8.G.B.8

3.

FLASHCARD QUESTION

Front

What are the side ratios of a 30-60-90 triangle?

Back

Tags

CCSS.HSG.CO.C.10

4.

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

5.

FLASHCARD QUESTION

Front

If one leg of a 45-45-90 triangle is 6, what is the length of the hypotenuse?

Back

Tags

CCSS.8.G.B.7

6.

FLASHCARD QUESTION

Front

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

Back

Tags

CCSS.8.G.B.8

7.

FLASHCARD QUESTION

Front

If the shorter leg of a 30-60-90 triangle is 4, what is the length of the longer leg?

Back

Tags

CCSS.HSG.CO.C.10

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