NTI Day 7- Flashcard Law of Sines, Cosines, and Area of a Triangle

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 its opposite angle 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 used to find a side when two sides and the included angle are known, and is expressed as: c² = a² + b² - 2ab*cos(C).

Front

How do you calculate the area of a triangle using the Law of Sines?

Back

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

Front

What is the formula for the area of a triangle given two sides and the included angle?

Back

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

Front

If angle A = 108 degrees, b = 32, and c = 27, how do you find the area of Triangle ABC?

Back

Use the formula: Area = (1/2) * b * c * sin(A). Plug in the values: Area = (1/2) * 32 * 27 * sin(108°).

Front

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

Back

In any triangle, the larger the angle, the longer the opposite side. This relationship is fundamental in using the Law of Sines and the Law of Cosines.

Front

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

Back

To solve for an unknown side, rearrange the Law of Sines: a/sin(A) = b/sin(B). If you know two angles and one side, you can find the other sides.

Front

What is the significance of the angle in the Law of Cosines?

Back

The angle in the Law of Cosines is crucial as it allows you to relate the lengths of the sides of the triangle. It is used when you have two sides and the included angle.

Front

How do you find the third angle in a triangle if two angles are known?

Back

The third angle can be found using the formula: C = 180° - A - B, where A and B are the known angles.

Front

What is the formula to find the length of a side using the Law of Cosines?

Back

To find the length of side c, use: c = √(a² + b² - 2ab*cos(C)).