Law of Sines and Cosines Word Problems

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

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

How do you find the area of a triangle using two sides and the included angle?

Back

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

Front

What is the formula to find the distance between two points using the Law of Sines?

Back

To find the distance between two points (A and B) using the Law of Sines, you can use: d = a * sin(B) / sin(A), where a is the distance from point A to the opposite angle.

Front

How do you solve for an unknown side in a triangle using the Law of Sines?

Back

To solve for an unknown side, rearrange the Law of Sines: a = b * (sin(A) / sin(B)).

Front

What is the significance of the included angle in triangle area calculations?

Back

The included angle is crucial because it directly affects the area calculation; different angles will yield different areas even with the same side lengths.

Front

How do you determine the height of a triangle using the area formula?

Back

The height (h) can be found using the formula: h = 2A / b, where A is the area and b is the base of the triangle.

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 apply the Law of Cosines to find an angle in a triangle?

Back

To find an angle, rearrange the Law of Cosines: C = cos⁻¹((a² + b² - c²) / (2ab)).

Front

What is the purpose of using the Law of Sines in real-world applications?

Back

The Law of Sines is used in navigation, surveying, and architecture to determine distances and angles that are not easily measurable.