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

In a triangle, the larger the angle, the longer the opposite side. Conversely, the smaller the angle, the shorter the opposite side.

How do you calculate the area of a triangle using the Law of Sines?

Area = (1/2) * a * b * sin(C), where a and b are two sides and C is the included angle.

What is the significance of the included angle in the Law of Cosines?

The included angle is the angle between the two sides used in the Law of Cosines formula, which is essential for calculating the third side.

When should you use the Law of Sines instead of the Law of Cosines?

Use the Law of Sines when you have two angles and one side (AAS or ASA) or two sides and a non-included angle (SSA).

When should you use the Law of Cosines instead of the Law of Sines?

Use the Law of Cosines when you have two sides and the included angle (SAS) or all three sides (SSS).

What is the formula to find the distance across a river using the Law of Cosines?

Use the formula: d = √(a² + b² - 2ab*cos(C)), where a and b are the lengths of the sides and C is the included angle.

How do you determine which law to use for a given triangle problem?

Identify the known values: if you have two angles and one side or two sides and a non-included angle, use the Law of Sines. If you have two sides and the included angle or all three sides, use the Law of Cosines.

What is the relationship between the angles and sides in the Law of Sines?

In the Law of Sines, the ratio of a side length to the sine of its opposite angle is constant, meaning larger angles correspond to larger opposite sides.

Law of Sines and Cosines

Flashcard

•

Mathematics

•

9th - 10th Grade

•

Practice Problem

•

Hard

•

CCSS

HSG.SRT.D.10, 8.G.A.5, HSG.CO.C.10

Standards-aligned

Wayground Content

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15 questions

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FLASHCARD QUESTION

Front

What is the Law of Sines?

Back

The Law of Sines states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is constant for all three sides and angles in the triangle. Formula: a/sin(A) = b/sin(B) = c/sin(C).

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

FLASHCARD QUESTION

Front

What is the Law of Cosines?

Back

The Law of Cosines relates the lengths of the sides of a triangle to the cosine of one of its angles. Formula: c² = a² + b² - 2ab*cos(C).

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

FLASHCARD QUESTION

Front

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

Back

To find a side length using the Law of Sines, use the formula: a/sin(A) = b/sin(B). Rearrange to find the unknown side.

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

FLASHCARD QUESTION

Front

How do you find an angle using the Law of Cosines?

Back

To find an angle using the Law of Cosines, rearrange the formula: cos(C) = (a² + b² - c²) / (2ab).

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

FLASHCARD QUESTION

Front

What is the formula for the Law of Sines?

Back

The formula for the Law of Sines is: a/sin(A) = b/sin(B) = c/sin(C).

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

FLASHCARD QUESTION

Front

What is the formula for the Law of Cosines?

Back

The formula for the Law of Cosines is: c² = a² + b² - 2ab*cos(C).

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

FLASHCARD QUESTION

Front

If m

Back

To find m

Tags

CCSS.8.G.A.5

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