B: Solving Problems using Trigonometry

If you need to solve a problem that requires trigonometry, it is important to sketch a diagram before trying to solve the problem. A diagram will help avoid the use of incorrect trigonometric ratios.

 

Example 1

Jon wants to walk from one corner of a square park, of length 100 m, to the opposite corner. How much farther, to the nearest tenth of a metre, is it to walk around the outside of the park than it is to cut directly across the park at a 45° angle?

Begin by sketching a diagram to represent the situation.

Each side of the park is 100 m in length, so if Jon walked around the outside of the park, he would have to walk 2 • 100 m = 200 m to get to the opposite corner.

To determine the diagonal distance, use either the sine ratio or the cosine ratio because the lengths of both legs of the right triangle are known.

The diagonal distance straight through the park is approximately 141 m.

It is approximately 58.6 m farther to walk around the park.