Triangle Area Calculation Using Sine Function

This video tutorial explains how to find the area of a triangle using the sine function, specifically when given two sides and the included angle (SAS). It covers three formulas involving sine, emphasizing the importance of the included angle. The derivation of the formula is demonstrated using right triangles and the sine function. Two example problems are solved, illustrating the application of the formula and the use of the law of sines to find missing angles. The video concludes with a summary of the method and its usefulness in solving triangle area problems.

What is the primary goal of using the sine function in triangle area calculation?

• To find the perimeter of a triangle

• To calculate the height of a triangle

• To find the length of the hypotenuse

• To determine the area of a triangle given two sides and the included angle

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

• The smallest angle

• Any angle of the triangle

• The largest angle

• The included angle between the two given sides

What is the formula for the area of a triangle using the sine function?

• Area = a * b * c

• Area = 1/2 * a * b * sin(C)

• Area = 1/2 * base * height

• Area = a + b + c

How is the height of a triangle related to the sine of an angle in the derivation of the area formula?

• Height is the product of the side and the sine of the angle

• Height is the sum of the side and the sine of the angle

• Height is the difference between the side and the sine of the angle

• Height is equal to the sine of the angle

In the first example problem, what is the measure of angle C?

• 63 degrees

• 82 degrees

• 35 degrees

• 45 degrees

What is the approximate area of the triangle in the first example problem?

• 40 square centimeters

• 60 square centimeters

• 30 square centimeters

• 50 square centimeters

In the second example problem, what method is used to find the missing angle?

• Pythagorean theorem

• Trigonometric identities

• Law of cosines

• Law of sines

What is the measure of angle A in the second example problem?

• 40 degrees

• 72 degrees

• 68 degrees

• 140 degrees

What is the approximate area of the triangle in the second example problem?

• 587 square feet

• 387 square feet

• 287 square feet

• 487 square feet

Why is the angle of 140 degrees not possible in the second example problem?

• It is not an included angle

• It exceeds the sum of 180 degrees with the other angles

• It is not a valid angle in any triangle

• It is less than 90 degrees