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

In a triangle, the larger the angle, the longer the side opposite that angle. This is a key principle in both the Law of Sines and the Law of Cosines.

What is the significance of the Law of Sines in non-right triangles?

The Law of Sines is particularly useful for solving non-right triangles, allowing for the calculation of unknown sides and angles when given sufficient information.

What is the significance of the Law of Cosines in non-right triangles?

The Law of Cosines is essential for solving triangles when two sides and the included angle are known, or when all three sides are known.

Example: Find the length of side BC if angle A = 30°, angle B = 60°, and side a = 10. (Use Law of Sines)

Using the Law of Sines: $$\frac{a}{\text{sin}(A)} = \frac{b}{\text{sin}(B) }$$ , we find side BC (b) = 10 * $$\frac{\text{sin}(60°)}{\text{sin}(30°)}$$ = 17.32.

Example: Use the Law of Cosines to find the value of x if a = 5, b = 7, and C = 60°.

Using the Law of Cosines: $$x^2 = 5^2 + 7^2 - 2(5)(7)\text{cos}(60°)$$ , we find x = 6.16.

What is the relationship between the Law of Sines and the Law of Cosines?

Both laws are used to solve triangles, but the Law of Sines is best for cases with two angles and one side, while the Law of Cosines is used for two sides and the included angle or all three sides.

Example: Find the measure of angle F if sides a = 8, b = 6, and c = 10. (Use Law of Cosines)

Using the Law of Cosines: $$\text{cos}(F) = \frac{8^2 + 6^2 - 10^2}{2(8)(6)}$$ , we find angle F = 45.57°.

What is the importance of understanding the Law of Sines and Law of Cosines in real-world applications?

Understanding these laws is crucial for fields such as engineering, architecture, and navigation, where precise measurements and calculations of angles and distances are necessary.

Law of Sines / Law of Cosines Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the Law of Sines?

Back

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

2.

FLASHCARD QUESTION

Front

What is the Law of Cosines?

Back

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

3.

FLASHCARD QUESTION

Front

How do you find a missing side using the Law of Sines?

Back

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

4.

FLASHCARD QUESTION

Front

How do you find a missing angle using the Law of Sines?

Back

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

5.

FLASHCARD QUESTION

Front

What is the formula for finding the area of a triangle using the Law of Sines?

Back

Tags

CCSS.HSG.SRT.D.9

6.

FLASHCARD QUESTION

Front

How do you apply the Law of Cosines to find a side?

Back

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

7.

FLASHCARD QUESTION

Front

How do you apply the Law of Cosines to find an angle?

Back

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

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