How can you determine if a triangle is solvable using the Law of Sines?

A triangle is solvable using the Law of Sines if you have at least one side and its opposite angle, or two angles and one side.

What is the ambiguous case in the Law of Sines?

The ambiguous case occurs in SSA situations where two different triangles may be formed, or no triangle can be formed at all.

How do you find the angle opposite a given side using the Law of Sines?

To find the angle opposite a given side, rearrange the Law of Sines to isolate the sine of the angle: $$\sin(A) = \frac{a \cdot \sin(B)}{b}$$ .

What is the formula to find a side using the Law of Sines?

To find a side using the Law of Sines, use the formula $$\frac{a}{\sin(A)} = \frac{b}{\sin(B)}$$ and solve for the unknown side.

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

The Law of Sines is important in fields such as engineering, navigation, and architecture, where determining distances and angles is crucial.

How do you check if your answer using the Law of Sines is reasonable?

Check if the calculated angles add up to 180 degrees and if the sides are proportional to the sine of their opposite angles.

What is the first step in solving a triangle using the Law of Sines?

Identify the known values (sides and angles) and determine which formula to use based on the given information.

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 more applicable for angle-side relationships, while the Law of Cosines is used for side-side relationships.

Law of Sines and Cosines Practice 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 does the Law of Sines help to find in a triangle?

Back

The Law of Sines helps to find unknown angles and sides in a triangle when given sufficient information (e.g., two angles and one side or two sides and a non-included angle).

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

3.

FLASHCARD QUESTION

Front

What is the formula for the Law of Cosines?

Back

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

4.

FLASHCARD QUESTION

Front

When is the Law of Cosines used instead of the Law of Sines?

Back

The Law of Cosines is used when you have two sides and the included angle (SAS) or all three sides (SSS) of a triangle, while the Law of Sines is used for AAS, ASA, or SSA cases.

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

5.

FLASHCARD QUESTION

Front

What is the significance of the angle-side relationship in the Law of Sines?

Back

In the Law of Sines, each side of a triangle is directly proportional to the sine of its opposite angle, meaning larger angles correspond to longer sides.

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

6.

FLASHCARD QUESTION

Front

How do you set up the Law of Sines to find an unknown angle?

Back

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

7.

FLASHCARD QUESTION

Front

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

Back

In a triangle, the side opposite the largest angle is the longest side, and the side opposite the smallest angle is the shortest side.

Tags

CCSS.HSG.CO.C.10

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