If one leg of a right triangle is 3 and the other leg is 4, what is the length of the hypotenuse?

Using the Pythagorean Theorem: $$c = \text{sqrt}(3^2 + 4^2) = \text{sqrt}(9 + 16) = \text{sqrt}(25) = 5$$ .

How do you find the missing side of a right triangle using the Pythagorean Theorem?

To find a missing side, rearrange the Pythagorean Theorem: If you know the hypotenuse (c) and one leg (a), use $$b = \text{sqrt}(c^2 - a^2)$$ . If you know both legs (a and b), use $$c = \text{sqrt}(a^2 + b^2)$$ .

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

In a right triangle, the larger the angle, the longer the opposite side. The smallest angle is opposite the shortest side.

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

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

If the sine of an angle is $$\frac{3}{5}$$ , what is the length of the opposite side if the hypotenuse is 10?

Using the sine ratio: $$\text{sine}(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$$ , we have: $$\frac{3}{5} = \frac{\text{opposite}}{10}$$ . Therefore, the opposite side is 6.

What is the relationship between sine, cosine, and tangent in a right triangle?

The relationships can be expressed as: $$\text{tan}(\theta) = \frac{\text{sine}(\theta)}{\text{cosine}(\theta)}$$ .

How do you round answers in geometry problems?

When rounding answers, look at the digit to the right of the desired decimal place. If it is 5 or greater, round up. If it is less than 5, round down.

Pythagorean Theorem and Rt triangle trig Flashcards

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14 questions

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1.

FLASHCARD QUESTION

Front

What is the Pythagorean Theorem?

Back

2.

FLASHCARD QUESTION

Front

How do you identify the hypotenuse in a right triangle?

Back

The hypotenuse is the longest side of a right triangle and is opposite the right angle.

3.

FLASHCARD QUESTION

Front

What is the definition of the opposite side in a right triangle?

Back

The opposite side is the side that is opposite to the angle of interest in a right triangle.

4.

FLASHCARD QUESTION

Front

What is the definition of the adjacent side in a right triangle?

Back

The adjacent side is the side that is next to the angle of interest in a right triangle, excluding the hypotenuse.

5.

FLASHCARD QUESTION

Front

What is the sine ratio in a right triangle?

Back

6.

FLASHCARD QUESTION

Front

What is the cosine ratio in a right triangle?

Back

7.

FLASHCARD QUESTION

Front

What is the tangent ratio in a right triangle?

Back

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