Calculating the Area of a Triangle using the Sine Rule

The video tutorial explains how to calculate the area of a triangle using the formula 1/2 ab sinC. It provides an example calculation, a proof of the formula using trigonometry, and a practical application for calculating the area of a field. Additionally, it demonstrates how to work backwards from a given area to find an angle. The tutorial emphasizes the importance of having two sides and the included angle for using this formula.

What is required to use the formula 1/2 ab sinC to find the area of a triangle?

• Three sides

• The base and the height

• Two sides and the included angle

• Two angles and a side

In the example calculation, what is the area of the triangle with sides 7 cm and 10 cm and an included angle of 73 degrees?

• 33.47 cm²

• 50.25 cm²

• 28.90 cm²

• 40.00 cm²

How is the height of a triangle calculated using trigonometry in the proof of the formula?

• B times sinC

• A times sinC

• B times cosC

• A times cosC

What is the purpose of using trigonometry in the proof of the area formula?

• To measure the angles

• To determine the hypotenuse

• To calculate the height when it is not perpendicular

• To find the base of the triangle

When calculating the area of a field by dividing it into triangles, what is the final step?

• Subtract the areas of the triangles

• Multiply the areas of the triangles

• Add the areas of the triangles

• Divide the areas of the triangles

If the area of a triangle is known, how can you find an unknown angle using the formula?

• By using the cosine rule

• By taking the inverse sine of the area divided by 1/2 of the product of the sides

• By using the tangent rule

• By dividing the area by the base

What is the calculated angle x if the area of a triangle is 215.67 m², with sides 24 m and 16 m?

• 86.83 degrees

• 75.00 degrees

• 90.00 degrees

• 60.00 degrees