How do you simplify the expression $$\text{√10} ⋅ \text{√45}$$ ?

To simplify $$\text{√10} ⋅ \text{√45}$$ , multiply the radicands: $$\text{√(10 * 45)} = \text{√450}$$ . Then, factor 450: $$\text{√(9 * 50)} = 3\text{√50}$$ .

What is the length of one leg in a 45-45-90 triangle if the hypotenuse is $$15\text{√2}$$ ?

In a 45-45-90 triangle, the legs are equal and each leg is $$\frac{hypotenuse}{\text{√2}}$$ . Therefore, if the hypotenuse is $$15\text{√2}$$ , each leg is 15.

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

In a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2. The shortest side is opposite the 30-degree angle, the longer leg is opposite the 60-degree angle, and the hypotenuse is twice the shortest side.

What is the value of $$\text{√(a^2 + b^2)}$$ when a = 3 and b = 4?

Using the Pythagorean theorem, $$\text{√(3^2 + 4^2)} = \text{√(9 + 16)} = \text{√25} = 5$$ .

How do you simplify $$\text{√(x^2)}$$ ?

The expression $$\text{√(x^2)}$$ simplifies to |x|, which is the absolute value of x.

What is the sine of an angle in a right triangle?

The sine of an angle (A) is the ratio of the length of the opposite side to the length of the hypotenuse: $$\text{sine(A)} = \frac{opposite}{hypotenuse}$$ .

What is the cosine of a 60-degree angle?

The cosine of a 60-degree angle is $$\frac{1}{2}$$ .

What is the tangent of an angle in a right triangle?

The tangent of an angle (A) is the ratio of the length of the opposite side to the length of the adjacent side: $$\text{tan(A)} = \frac{opposite}{adjacent}$$ .

How do you calculate the perimeter of a triangle?

The perimeter (P) of a triangle is the sum of the lengths of all three sides: $$P = a + b + c$$ .

What is the formula for the volume of a rectangular prism?

The volume (V) of a rectangular prism can be calculated using the formula: $$V = length \times width \times height$$ .

Mixed Practice Flashcards

Student preview

15 questions

Show all answers

1.

FLASHCARD QUESTION

Front

What is the Pythagorean theorem?

Back

Tags

CCSS.8.G.B.8

2.

FLASHCARD QUESTION

Front

Back

3.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.8.G.B.8

4.

FLASHCARD QUESTION

Front

If the short side of a right triangle is 25, how do you find the hypotenuse?

Back

Tags

CCSS.8.G.B.7

5.

FLASHCARD QUESTION

Front

Back

This represents the cosine of angle A, which is the ratio of the length of the adjacent side (40) to the length of the hypotenuse (50). Cosine values range from -1 to 1.

Tags

CCSS.HSG.SRT.C.6

6.

FLASHCARD QUESTION

Front

What is the formula for the area of a triangle?

Back

Tags

CCSS.6.G.A.1

7.

FLASHCARD QUESTION

Front

How do you find the length of the hypotenuse in a right triangle?

Back

Tags

CCSS.8.G.B.7

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