M2: 5.5-5.6 Flashcard

Front

What is the Law of Cosines?

Back

The Law of Cosines states that in any triangle, the square of the length of one side is equal to the sum of the squares of the lengths of the other two sides minus twice the product of those lengths and the cosine of the included angle. It is used to find unknown side lengths or angles in triangles.

Front

What is the formula to calculate the distance between two points using the Law of Cosines?

Back

c² = a² + b² - 2ab * cos(C), where c is the side opposite angle C, and a and b are the other two sides.

Front

What is an included angle in a triangle?

Back

An included angle is the angle formed between two sides of a triangle.

Front

How do you find the distance across a river using the Law of Cosines?

Back

You can find the distance across the river by treating the problem as a triangle where the sides are the distances from two points on one side of the river to a point on the opposite side, and the included angle is the angle between those two lines.

Front

What is the angle of elevation?

Back

The angle of elevation is the angle formed by the horizontal line and the line of sight to an object above the horizontal.

Front

How do you calculate the distance to an object using the angle of elevation?

Back

You can use trigonometric functions, specifically the tangent function, where distance = height / tan(angle of elevation).

Front

What is the significance of the angle in triangle problems?

Back

The angles in a triangle are crucial for determining the relationships between the sides and for applying the Law of Sines and Law of Cosines.

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.

Front

What is the formula for the Law of Sines?

Back

a/sin(A) = b/sin(B) = c/sin(C), where a, b, and c are the lengths of the sides opposite angles A, B, and C respectively.

Front

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

Back

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