HW: Dec 12 Law of Sines

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: a/sin(A) = b/sin(B) = c/sin(C).

Front

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

Back

To find a missing side, rearrange the Law of Sines formula: a = (b * sin(A)) / sin(B), where A and B are the angles opposite sides a and b, respectively.

Front

If angle A = 30° and angle B = 60°, how do you find angle C?

Back

Use the triangle sum theorem: C = 180° - A - B = 180° - 30° - 60° = 90°.

Front

Given a triangle with sides a = 10, b = 14, and angle A = 30°, how do you find angle B?

Back

Use the Law of Sines: sin(B) = (b * sin(A)) / a. Calculate B using the inverse sine function.

Front

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

Back

In a triangle, larger angles are opposite longer sides, and smaller angles are opposite shorter sides.

Front

How can the Law of Sines be used to solve for an unknown angle?

Back

Rearrange the Law of Sines: sin(B) = (b * sin(A)) / a, then use the inverse sine function to find angle B.

Front

What is the formula for the Law of Sines?

Back

The formula is: a/sin(A) = b/sin(B) = c/sin(C), where a, b, and c are the sides of the triangle and A, B, and C are the angles.

Front

If angle A = 45° and side a = 10, how do you find side b if angle B = 60°?

Back

Use the Law of Sines: b = (a * sin(B)) / sin(A). Substitute the values to find b.

Front

What is the significance of the Law of Sines in solving triangles?

Back

The Law of Sines allows for the calculation of unknown sides and angles in non-right triangles, making it essential for triangle solving.

Front

How do you determine if a triangle is solvable with the Law of Sines?

Back

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