If the opposite side is 4 and the hypotenuse is 5, what is the angle using sine?

Using sine: $$\theta = \text{sin}^{-1}igg(\frac{4}{5}igg) \text{ which is approximately } 53.1^\text{o}$$ .

If the adjacent side is 3 and the hypotenuse is 5, what is the angle using cosine?

Using cosine: $$\theta = \text{cos}^{-1}igg(\frac{3}{5}igg) \text{ which is approximately } 53.1^\text{o}$$ .

If the opposite side is 3 and the adjacent side is 4, what is the angle using tangent?

Using tangent: $$\theta = \text{tan}^{-1}igg(\frac{3}{4}igg) \text{ which is approximately } 36.9^\text{o}$$ .

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 can you use the Pythagorean theorem to find a missing side?

To find a missing side, rearrange the Pythagorean theorem: If $$c$$ is the hypotenuse and $$a$$ is one side, then $$b = \text{sqrt}(c^2 - a^2)$$ .

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

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

What is the range of values for sine, cosine, and tangent?

The range of sine and cosine is between -1 and 1. The range of tangent is all real numbers.

How do you convert degrees to radians?

To convert degrees to radians, use the formula: $$\text{radians} = \text{degrees} \times \frac{\text{π}}{180}$$ .

Using Trig to find Missing Angles and Sides Flashcards

Student preview

15 questions

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1.

FLASHCARD QUESTION

Front

What is the definition of sine in a right triangle?

Back

Tags

CCSS.HSG.SRT.C.6

2.

FLASHCARD QUESTION

Front

What is the definition of cosine in a right triangle?

Back

Tags

CCSS.HSG.SRT.C.6

3.

FLASHCARD QUESTION

Front

What is the definition of tangent in a right triangle?

Back

Tags

CCSS.HSG.SRT.C.6

4.

FLASHCARD QUESTION

Front

What is the purpose of inverse trigonometric functions?

Back

Inverse trigonometric functions are used to find the angle when the values of the sides are known. They allow us to solve for angles in right triangles.

Tags

CCSS.HSG.SRT.C.8

5.

FLASHCARD QUESTION

Front

How do you find the missing angle in a right triangle using sine?

Back

Tags

CCSS.HSG.SRT.C.8

6.

FLASHCARD QUESTION

Front

How do you find the missing angle in a right triangle using cosine?

Back

Tags

CCSS.HSG.SRT.C.8

7.

FLASHCARD QUESTION

Front

How do you find the missing angle in a right triangle using tangent?

Back

Tags

CCSS.HSG.SRT.C.8

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