Triangle Area and Angle Calculations

The video introduces a formula for calculating the area of a triangle using two sides and the included angle, A = 1/2 ab sin C. It provides a detailed explanation and example calculation, emphasizing the formula's usefulness when the triangle's height is unknown. A practice problem is also presented, demonstrating the formula's application to an isosceles triangle.

What is the traditional formula for finding the area of a triangle?

• 1/2 * a * b * sin(C)

• a * b * sin(C)

• base * height

• 1/2 * base * height

Which formula is introduced for finding the area of a triangle using sine?

• 1/2 * base * height

• 1/2 * a * b * sin(C)

• a * b * sin(C)

• 1/2 * a * b * cos(C)

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

• The base of the triangle

• The height of the triangle

• The hypotenuse of the triangle

• The included angle between sides a and b

What are the given side lengths in the example problem?

• 5 cm and 6 cm

• 4 cm and 5 cm

• 6 cm and 7 cm

• 3 cm and 4 cm

What is the included angle in the example problem?

• 45 degrees

• 32 degrees

• 60 degrees

• 30 degrees

Why is it important to check the angular mode on your calculator?

• To ensure the calculator is in scientific mode

• To ensure the calculator is in degree or radian mode as required

• To ensure the calculator is in graphing mode

• To ensure the calculator is in basic mode

What is the calculated area of the triangle in the example problem?

• 5.3 cm²

• 7.1 cm²

• 4.5 cm²

• 6.2 cm²

What type of triangle is used in the practice problem?

• Equilateral triangle

• Scalene triangle

• Isosceles triangle

• Right triangle

What are the side lengths of the triangle in the practice problem?

• 7 cm and 7 cm

• 6 cm and 6 cm

• 8 cm and 8 cm

• 5 cm and 5 cm

What is the given angle in the practice problem?

• 80 degrees

• 60 degrees

• 70 degrees

• 90 degrees