Law of Sines Practice

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 use the Law of Sines to find an unknown side?

Back

To find an unknown side using the Law of Sines, rearrange the formula to isolate the side: a = (b * sin(A)) / sin(B).

Front

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

Back

The area (A) of a triangle can be calculated using the formula: A = (1/2) * a * b * sin(C), where a and b are two sides and C is the included angle.

Front

What is the relationship between 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 you determine if a triangle is solvable with the Law of Sines?

Back

A triangle is solvable with the Law of Sines if you have either two angles and one side (AAS or ASA) or two sides and a non-included angle (SSA).

Front

What does it mean if a triangle has no solution using the Law of Sines?

Back

If a triangle has no solution, it means that the given information does not correspond to a valid triangle, often occurring in SSA cases where the angle does not allow for a triangle to be formed.

Front

What is the significance of the ambiguous case in the Law of Sines?

Back

The ambiguous case occurs in SSA situations where two different triangles may be possible, one triangle, or no triangle at all, depending on the given values.

Front

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

Back

To find a missing angle, use the Law of Sines to set up the ratio and then apply the inverse sine function: A = sin^(-1)(a * sin(B) / b).

Front

What is the sine of 90 degrees?

Back

The sine of 90 degrees is 1.

Front

What is the sine of 0 degrees?

Back

The sine of 0 degrees is 0.