Mr. Pleacher had an unusually shaped garden because it was in the back corner of his lot. It was nearly impossible to see the shape of the garden from ground level, so he put in several stakes at the 4 corners of his garden (called A, B, C, and D in the diagram below). Then he made some measurements and drew a picture of the garden. In order to make a scaled drawing of the garden, he needed to find the measures of some angles using the Law of Cosines. Determine the measures of angle C and angle ABD using the following measurements: AB = 460", AD = 330", CD = 382", BC = 454", and BD = 610". The garden is NOT rectangular shaped and this picture is not drawn to scale.
Solution to the Problem:
Angle C has a measure of 93.3 degrees and angle ABD has a measure of 32.2 degrees.Use the Law of cosines to solve for both angles:
Here is the scale drawing of Mr. P's garden.
Correctly solved by:
| 1. James Alarie | Flint, Michigan |
| 2. Trenton Harmon |
Mountain View High School, Mountain View, Wyoming |
| 3. Larissa Giessinger |
Mountain View High School, Mountain View, Wyoming |
| 4. Brian Morrison |
Thornton Academy, Saco, Maine |
| 5. Vikash Kumar | New Delhi, India |