Triangle Area and Trigonometry Concepts

The video tutorial explains how to calculate the area of a triangle using the formula 'area = 1/2 * base * height'. It highlights the importance of using the perpendicular height and introduces a trigonometric approach to find the area of any triangle using the formula 'area = 1/2 * a * b * sin(C)'. The tutorial covers the derivation of this formula and its application, emphasizing the use of the included angle between two sides.

What is the formula for calculating the area of a triangle using its base and height?

• Area = base + height

• Area = base * height

• Area = 1/2 * base * height

• Area = base / height

Why is the perpendicular height important in calculating the area of a triangle?

• It is used to find the perimeter.

• It is always equal to the base.

• It ensures the area calculation is accurate.

• It is the longest side of the triangle.

What is the term used for the height of a triangle when it is not right-angled?

• Altitude

• Diagonal

• Base

• Hypotenuse

How can trigonometry help in finding the area of a non-right angled triangle?

• By using the cosine of the angle

• By using the tangent of the angle

• By using the secant of the angle

• By using the sine of the angle

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

• Area = a * b * sec(C)

• Area = a * b * tan(C)

• Area = 1/2 * a * b * sin(C)

• Area = 1/2 * a * b * cos(C)

What does the term 'included angle' refer to in a triangle?

• The smallest angle in the triangle

• The angle between two given sides

• The angle opposite the shortest side

• The angle opposite the longest side

Why is it important to use the included angle in the area formula for triangles?

• It is always 90 degrees.

• It ensures the formula is applied correctly.

• It is the only angle that can be measured.

• It is the largest angle in the triangle.

What happens if you use a non-included angle in the area formula for triangles?

• The calculation will be unaffected.

• The calculation will be incorrect.

• The area will be underestimated.

• The area will be overestimated.

Which of the following is NOT a requirement for using the formula 1/2 * a * b * sin(C)?

• Knowing the included angle

• Knowing two sides of the triangle

• Using the sine function

• Having a right-angled triangle

What is the benefit of using the formula 1/2 * a * b * sin(C) for triangle area?

• It requires no angles.

• It can be used for any triangle.

• It only works for right-angled triangles.

• It simplifies to a linear equation.