Julia's Practice Flashcard

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 given by the formula: c² = a² + b² - 2ab * cos(C), where C is the angle opposite side c.

Front

How do you find the length of a side in a triangle using the Law of Cosines?

Back

To find the length of a side, rearrange the Law of Cosines formula to solve for the desired side. For example, to find side c: c = √(a² + b² - 2ab * cos(C)).

Front

What is the formula for finding the area of a triangle using the lengths of its sides?

Back

The area A of a triangle can be calculated using Heron's formula: A = √(s(s-a)(s-b)(s-c)), where s is the semi-perimeter, s = (a+b+c)/2.

Front

What is a semi-perimeter in the context of a triangle?

Back

The semi-perimeter of a triangle is half the sum of the lengths of its sides, calculated as s = (a + b + c) / 2.

Front

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

Back

In a triangle, the larger the angle, the longer the opposite side. This is known as the triangle inequality theorem.

Front

How do you calculate the angle of a triangle using the Law of Cosines?

Back

To find an angle, rearrange the Law of Cosines formula: cos(C) = (a² + b² - c²) / (2ab). Then use the inverse cosine function.

Front

What is the Pythagorean theorem?

Back

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b): c² = a² + b².

Front

What is the significance of the 30-60-90 triangle?

Back

In a 30-60-90 triangle, the ratios of the lengths of the sides are 1:√3:2. The side opposite the 30° angle is the shortest.

Front

What is the significance of the 45-45-90 triangle?

Back

In a 45-45-90 triangle, the lengths of the legs are equal, and the hypotenuse is √2 times the length of each leg.

Front

What is the formula for the perimeter of a triangle?

Back

The perimeter P of a triangle is the sum of the lengths of its sides: P = a + b + c.