1.6 Laws of Sine and Cosine Practice

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 of the triangle. It is expressed as: a/sin(A) = b/sin(B) = c/sin(C).

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. It is expressed as: c² = a² + b² - 2ab*cos(C).

Front

Can you find all the angles of a triangle given its three sides?

Back

Yes, you can use the Law of Cosines to find the angles if you know all three sides.

Front

How many possible triangles can be formed with m

Back

2 possible triangles can be formed.

Front

How many possible triangles can be formed with m

Back

2 possible triangles can be formed.

Front

How many possible triangles can be formed with m

Back

0 possible triangles can be formed.

Front

What is the relationship between the angles and sides in a triangle according to the Law of Sines?

Back

The Law of Sines shows that the ratio of a side length to the sine of its opposite angle is the same for all three sides.

Front

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

Back

The ambiguous case occurs when two sides and a non-included angle are known, leading to potentially two different triangles.

Front

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

Back

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

Front

What is the first step to determine if a triangle can be formed with given dimensions?

Back

Check if the sum of the lengths of any two sides is greater than the length of the third side.