Area of Triangle with Two Sides

This video tutorial explains how to find the area of a triangle when given two sides and the included angle. The instructor begins by introducing the concept and then derives the formula for the area using the sine rule. The formula is explained as 1/2 * a * b * sin(C), where a and b are the sides, and C is the included angle. The video includes examples to demonstrate the application of the formula, ensuring that viewers understand how to calculate the area in different scenarios. The session concludes with an invitation for questions.

What is the main topic discussed in this session?

• Area of a rectangle

• Area of a triangle with two sides and an included angle

• Volume of a cylinder

• Perimeter of a square

What is the first step in deriving the formula for the area of a triangle with two sides and an included angle?

• Calculating the perimeter

• Identifying the base and height

• Using the Pythagorean theorem

• Proving the formula

In the formula derivation, what is used to find the height of the triangle?

• Cosine rule

• Tangent rule

• Sine rule

• Pythagorean theorem

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

• a^2 + b^2 = c^2

• 1/2 * base * height

• a * b * c

• 1/2 * a * b * sin(C)

In the formula 1/2 * a * b * sin(C), what does 'C' represent?

• The hypotenuse of the triangle

• The included angle between sides a and b

• The height of the triangle

• The base of the triangle

What is the significance of the included angle in the formula?

• It is used in the sine function to find the area

• It is irrelevant to the formula

• It determines the base of the triangle

• It is used to calculate the height

Why is the sine function used in the formula for the area of a triangle?

• To find the hypotenuse

• To find the perimeter

• To determine the height using the included angle

• To calculate the base

What is the role of the '1/2' in the formula 1/2 * a * b * sin(C)?

• It is a constant for all triangle area calculations

• It accounts for the triangle's height

• It ensures the formula calculates the correct area

• It adjusts the formula for a right triangle

In the context of the formula, what do 'a' and 'b' represent?

• The two sides of the triangle

• The angles of the triangle

• The base and height of the triangle

• The hypotenuse and one side

How does the formula 1/2 * a * b * sin(C) differ from the basic area formula 1/2 * base * height?

• It is only for right triangles

• It uses the cosine function instead of sine

• It applies to all polygons

• It incorporates an angle to find height