Chapter 6 - More Trig

Front

What is the Law of Sines?

Back

The Law of Sines states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant. It can be expressed as: \( \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} \).

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Front

How do you find the cosine of an angle in a right triangle?

Back

In a right triangle, the cosine of an angle is defined as the ratio of the length of the adjacent side to the length of the hypotenuse. It can be expressed as: \( \cos A = \frac{\text{adjacent}}{\text{hypotenuse}} \).

Tags

CCSS.HSG.SRT.C.6

Front

What is the formula for 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. It is given by: \( c^2 = a^2 + b^2 - 2ab \cos C \).

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Front

How do you solve for a missing angle in a triangle using the Law of Sines?

Back

To solve for a missing angle using the Law of Sines, rearrange the formula to find the angle: \( \sin A = \frac{a \cdot \sin B}{b} \) and use the inverse sine function.

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Front

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

Back

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

Tags

CCSS.HSG.CO.C.10

Front

What is the significance of the hypotenuse in a right triangle?

Back

The hypotenuse is the longest side of a right triangle, opposite the right angle, and is used in trigonometric ratios to define sine, cosine, and tangent.

Front

How can you find the length of a side in a triangle using the Law of Cosines?

Back

To find the length of a side using the Law of Cosines, use the formula: \( c = \sqrt{a^2 + b^2 - 2ab \cos C} \).

Tags

CCSS.HSG.SRT.D.11

CCSS.HSG.SRT.D.10

Front

What is the sine of an angle in a right triangle?

Back

The sine of an angle is defined as the ratio of the length of the opposite side to the length of the hypotenuse. It can be expressed as: \( \sin A = \frac{\text{opposite}}{\text{hypotenuse}} \).

Tags

CCSS.HSG.SRT.C.6

Front

What is the purpose of the Law of Cosines?

Back

The Law of Cosines is used to find a side or angle in any triangle when you know two sides and the included angle or all three sides.

Tags

CCSS.HSG.SRT.D.11

CCSS.HSG.SRT.D.10

Front

How do you apply the Law of Sines to find an unknown side?

Back

To find an unknown side using the Law of Sines, rearrange the formula: \( a = \frac{b \cdot \sin A}{\sin B} \).

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11