If sin(30°) = 0.5, what is the length of the opposite side if the hypotenuse is 10?

Using the sine formula: $$\text{Opposite} = \text{Hypotenuse} \times \text{sin}(30°) = 10 \times 0.5 = 5$$ .

If cos(60°) = 0.5, what is the length of the adjacent side if the hypotenuse is 8?

Using the cosine formula: $$\text{Adjacent} = \text{Hypotenuse} \times \text{cos}(60°) = 8 \times 0.5 = 4$$ .

If tan(45°) = 1, what is the length of the opposite side if the adjacent side is 7?

Using the tangent formula: $$\text{Opposite} = \text{Adjacent} \times \text{tan}(45°) = 7 \times 1 = 7$$ .

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

In a right triangle, the angles determine the ratios of the sides. The larger the angle, the longer the opposite side relative to the adjacent side.

How do you solve for an angle using the Sine function?

To solve for an angle using Sine, use the inverse sine function: $$\theta = \text{sin}^{-1}igg(\frac{O}{H}igg)$$ .

How do you solve for an angle using the Cosine function?

To solve for an angle using Cosine, use the inverse cosine function: $$\theta = \text{cos}^{-1}igg(\frac{A}{H}igg)$$ .

How do you solve for an angle using the Tangent function?

To solve for an angle using Tangent, use the inverse tangent function: $$\theta = \text{tan}^{-1}igg(\frac{O}{A}igg)$$ .

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

In a 30-60-90 triangle, the sides are in the ratio 1:√3:2, which simplifies calculations involving angles of 30° and 60°.

Finding Sides and Angles using Trigonometry Flashcards

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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

How do you find the length of a side using the Sine function?

Back

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

5.

FLASHCARD QUESTION

Front

How do you find the length of a side using the Cosine function?

Back

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

6.

FLASHCARD QUESTION

Front

How do you find the length of a side using the Tangent function?

Back

Tags

CCSS.HSG.SRT.C.8

7.

FLASHCARD QUESTION

Front

What is the Pythagorean theorem?

Back

Tags

CCSS.8.G.B.8

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