"The Right Angle"

Story Summary

Mr. Wendell, the math teacher, comes onto the field and tells Ryan that he is concerned about Ryan's geometry grades. If Ryan does not pass Friday's test, he will not be allowed to participate in Monday's championship baseball game. Jasper Woodbury, a local newspaper reporter, joins Mr. Wendell and Ryan. After Mr. Wendell promises to meet Ryan in the study lab the next day to help him with geometry, he leaves with Jasper to be interviewed about the new computer lab. Ryan then joins Paige, who is busy marking off a softball field. They discuss the differences in size between softball and baseball diamonds.

In the study lab the following day, Paige shows Ryan how she is using a topographic map to help her follow the directions and clues her grandfather left her so she can pinpoint the location of the cave. Her grandfather's directions are good only one month of the year, and now is the time. The first direction says that the cave is within an 8-mile radius of the home of her Native American ancestors. Another clue says to stand at the northeast bank of the spot where two rivers meet and go to the nearest rock formation at a bearing of 20 degrees. Paige shows Ryan how she can use a compass or a bearing guide to project bearings on the map.

Mr. Wendell comes into the study lab to work with Ryan on geometry. Ryan's assignment was to make conjectures about some triangles that he likes. Ryan talks about the geometry of baseball and softball fields. He knows that triangles with two equal sides are called isosceles triangles. He makes a conjecture that any time a right triangle has a 45-degree angle it has to be isosceles. Ryan tests this conjecture by folding different pieces of paper into triangles.

After Mr. Wendell leaves, Paige tells Ryan how her grandfather used principles of geometry to estimate the height of tall objects, like trees and cliffs. Paige expresses her frustration at not being able to figure out the map because she wants so badly to find the gift her grandfather left for her in the cave.

Paige goes to Larry's barn, where she boards her horse, and finds Larry feeding his horse. She notices a sundial outside, and Larry explains how it can be used to tell time. He demonstrates how shadows can be used to measure the height of a tall pole. Then, he shows Paige a different method for estimating the height of the barn. He uses a tape measure, an instrument he made to measure angles, graph paper and a protractor. Larry happens to mention Two Rivers Junction where he likes to fish. When Paige expresses interest in it, he explains that the river was rerouted 10 years ago and no longer has a junction there. On the map, he points out the place where the two rivers once met.

Later, Paige and Ryan are working again in the study lab. Paige tells Ryan she has figured out the location of the cave on her map and asks Ryan to ride out there with her. They agree to meet at Larry's barn at 6:00 the next morning, which is Saturday.

Unfortunately, as Ryan is riding his bicycle to Larry's on Saturday morning, he gets a flat tire and can't make it there in time to leave with Paige. Paige waits at Larry's barn until 6:30 a.m., and Larry decides to go with her in place of Ryan.

They finally find the cave, and Paige is excited with her gift, a beautiful necklace. Suddenly, Larry's horse is spooked by a snake, and Larry is thrown off while the horse runs away. When Paige sees Larry, he is lying on the ground unconscious. Paige quickly writes a note to Ryan, puts it in the saddlebag, and sends her horse back to the barn.

At 3:00 p.m., Mr. Wendell goes to the barn, where he has arranged to meet Larry to borrow some camping equipment. Mr. Wendell finds two saddled horses, but Larry is not around. He also finds the note from Paige, her map and the directions to the cave in the saddlebag. Following Paige's instructions in the note, Mr. Wendell calls Ryan to join him at the barn as quickly as possible.

Ryan arrives and tells Mr. Wendell that using the map and the directions, they can find Paige and Larry. They decide to take Mr. Wendell's Jeep and to contact the rescue squad to meet them there. The rescue squad is located 10 miles southwest of Two Rivers Junction. Squad members cannot use the helicopter because it is storming outside, but they can use their truck. Both the Jeep and the truck can go approximately 50 mph on the roads and 25 mph off-road. Mr. Wendell predicts that the rescue squad members may not have a map of the wilderness area where the cave is located, but they will probably have a compass.

Challenge

• What were the directions?
• Be as exact as possible.