What is the height of a cone if the radius is 5 cm and the slant height is 13 cm?

Using the Pythagorean Theorem: $$h = \text{sqrt}(l^2 - r^2) = \text{sqrt}(13^2 - 5^2) = \text{sqrt}(169 - 25) = \text{sqrt}(144) = 12 \text{ cm}$$ .

What is the formula for the area of a triangle?

The area of a triangle can be calculated using the formula: $$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$$ .

If the base of a triangle is 10 cm and the height is 5 cm, what is the area?

Using the area formula: $$\text{Area} = \frac{1}{2} \times 10 \times 5 = 25 \text{ cm}^2$$ .

What is the distance formula in a coordinate plane?

The distance between two points (x1, y1) and (x2, y2) is given by: $$d = \text{sqrt}((x2 - x1)^2 + (y2 - y1)^2)$$ .

How do you find the missing side of a right triangle if you know the other two sides?

Use the Pythagorean Theorem: If you know sides a and b, find c using $$c = \text{sqrt}(a^2 + b^2)$$ . If you know c and one side, rearrange to find the missing side.

What is the definition of a right triangle?

A right triangle is a triangle that has one angle measuring 90 degrees.

What is the significance of the 30-60-90 triangle?

In a 30-60-90 triangle, the sides are in the ratio 1 : $$\text{sqrt}(3) : 2$$ , where 1 is the length of the side opposite the 30-degree angle, $$\text{sqrt}(3)$$ is opposite the 60-degree angle, and 2 is the hypotenuse.

What is the significance of the 45-45-90 triangle?

In a 45-45-90 triangle, the sides are in the ratio 1 : 1 : $$\text{sqrt}(2)$$ , where the legs are equal and the hypotenuse is $$\text{sqrt}(2)$$ times the length of each leg.

Pythagorean Theorem and Trig Review Flashcards

Student preview

15 questions

Show all answers

1.

FLASHCARD QUESTION

Front

What is the Pythagorean Theorem?

Back

2.

FLASHCARD QUESTION

Front

What is the sine ratio in a right triangle?

Back

3.

FLASHCARD QUESTION

Front

What is the cosine ratio in a right triangle?

Back

4.

FLASHCARD QUESTION

Front

What is the tangent ratio in a right triangle?

Back

5.

FLASHCARD QUESTION

Front

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

Back

6.

FLASHCARD QUESTION

Front

If one side of a right triangle is 6 and the other side is 8, what is the length of the hypotenuse?

Back

7.

FLASHCARD QUESTION

Front

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

Back

In a right triangle, the side opposite the largest angle is the longest side (the hypotenuse), and the side opposite the smallest angle is the shortest side.

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