Triangle Area and Trigonometric Functions

The video tutorial explains how to calculate the area of a triangle using the traditional base and height method and introduces a trigonometric approach using the sine of an angle. The instructor demonstrates how to substitute the height with a trigonometric expression, allowing the calculation of the area with two sides and the included angle. An example calculation is provided to illustrate the process.

What is the basic formula for calculating the area of a triangle?

• Half base times height

• Base minus height

• Base times height

• Base plus height

What is the term used for the perpendicular line from the base to the opposite vertex in a triangle?

• Bisector

• Median

• Hypotenuse

• Altitude

In a right-angled triangle, what trigonometric function relates the opposite side to the hypotenuse?

• Cosine

• Tangent

• Sine

• Secant

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

• a b cosine c

• a b sine c

• Half a b cosine c

• Half a b sine c

Why is it unnecessary to know the height when using the sine formula for the area of a triangle?

• The formula uses two sides and an angle

• The formula is independent of any measurements

• The formula directly uses the base and height

• The formula only requires one side

Which angle is used in the formula half a b sine c for calculating the area of a triangle?

• The smallest angle

• The largest angle

• Any angle in the triangle

• The included angle between sides a and b

What is the significance of the included angle in the sine formula for the area of a triangle?

• It is the largest angle in the triangle

• It is the smallest angle in the triangle

• It is the angle between the two given sides

• It is the angle opposite the base

In the example calculation, what is the approximate area of the triangle to one decimal place?

• 50.0 square centimeters

• 60.0 square centimeters

• 55.5 square centimeters

• 52.2 square centimeters

What units are used for the area in the example calculation?

• Square feet

• Square centimeters

• Square inches

• Square meters

How does the sine formula for the area of a triangle relate to the sine rule?

• Both require the same number of angles

• Both are used for right-angled triangles

• Both use the sine of an angle

• Both require the same number of sides