Finding the Area of a Triangle Using Trigonometry
Explore how the area of a triangle relates to two side lengths and the sine of their included angle.
Task 1
Putting It All Together
Answer these open ended questions on your own or with others to form deeper math connections.
Task 2
Two sides of a triangular paddock measure 20 and 15 yards, and the angle between them is 45°. Find the area of the paddock.
Task 3
Two sides of a triangular paddock measure 20 and 15 yards, and the sine of the angle between them is 4/5. Without calculating the area, can you determine which paddock has the greater area: this one or the one in the previous problem? Verify your conjecture by calculating the area of this paddock.