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

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

How do you solve for a side in a right triangle using trigonometric ratios?

Use the appropriate trigonometric ratio (sine, cosine, or tangent) based on the known angle and the sides involved.

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

Each leg is $$\frac{10}{\text{sqrt}(2)}$$ or approximately 7.07.

What is the Pythagorean theorem?

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

How do you find the area of a right triangle?

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

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

The sum of the angles in any triangle is 180 degrees. In a right triangle, one angle is 90 degrees, so the other two angles must sum to 90 degrees.

If the lengths of the legs of a right triangle are 3 and 4, what is the length of the hypotenuse?

Using the Pythagorean theorem, the hypotenuse is 5, since $$3^2 + 4^2 = 5^2$$ .

What is the significance of special right triangles in trigonometry?

Special right triangles provide easy reference ratios for sine, cosine, and tangent, making calculations simpler.

Special Right Triangles and Trig Ratios Practice 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 30-60-90 triangle is 4, what is the length of the hypotenuse?

Back

The hypotenuse is 8, since it is twice the length of the shorter leg.

Tags

CCSS.HSG.CO.C.10

6.

FLASHCARD QUESTION

Front

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

Back

Tags

CCSS.HSG.SRT.C.6

7.

FLASHCARD QUESTION

Front

What is the formula for the cosine of an angle in a right triangle?

Back

Tags

CCSS.HSG.SRT.C.6

Access all questions and much more by creating a free account

Create resources

Host any resource

Get auto-graded reports

Continue with Google

Continue with Email

Continue with Classlink

Continue with Clever

or continue with

Microsoft

Apple

Others

Already have an account?

Similar Resources on Wayground

10 questions

Listening Practice

Flashcard

•

10th Grade

10 questions

The Role of Joints and Types of Synovial Joints

Flashcard

•

10th Grade

5 questions

Flashcard on Atomic Structure

Flashcard

•

10th Grade

9 questions

Classical and Medieval Art

Flashcard

•

KG

10 questions

Present Simple - Negative

Flashcard

•

10th Grade

10 questions

Biomolecules Review

Flashcard

•

9th Grade

Popular Resources on Wayground

10 questions

5.P.1.3 Distance/Time Graphs

Quiz

•

5th Grade

10 questions

Fire Drill

Quiz

•

2nd - 5th Grade

20 questions

Equivalent Fractions

Quiz

•

3rd Grade

15 questions

Hargrett House Quiz: Community & Service

Quiz

•

5th Grade

20 questions

Main Idea and Details

Quiz

•

5th Grade

20 questions

Context Clues

Quiz

•

6th Grade

20 questions

Inferences

Quiz

•

4th Grade

15 questions

Equivalent Fractions

Quiz

•

4th Grade

Discover more resources for Mathematics

10 questions

Exploring Basic Probability Concepts

Interactive video

•

6th - 10th Grade

16 questions

Identifying Angles

Quiz

•

7th - 12th Grade

25 questions

Complementary and Supplementary Angles

Quiz

•

7th - 10th Grade

15 questions

Exponential Growth and Decay Word Problems Practice

Quiz

•

9th - 12th Grade

10 questions

Calculating the Volume of Rectangular Prisms

Interactive video

•

6th - 10th Grade

20 questions

Central Angles and Arc Measures

Quiz

•

9th - 12th Grade

10 questions

Factor Quadratic Expressions with Various Coefficients

Quiz

•

9th - 12th Grade

30 questions

Intro to Circles Vocabulary

Quiz

•

9th - 12th Grade