In the 1998-99 school year our trig students did a class project, which was to build a three dimensional map of the nearby stars, showing where they are in space.

Much of trig is simple memorization (so are many important life skills), and although low-level thinking isn’t trendy I don’t see anything wrong with teaching those aspects.  Sometimes on a Friday we played Trig Concentration, which usually seems to engage the class and promote some learning.

Some good trig problems:

(Pythagorean Theorem)  Alan and Bert are standing on the southern side of a wall that runs east and west, 120 meters long.  They decide to race to a certain tree, which is 450 meters due north of the east end wall.  Bert goes east around the wall and then heads straight for the tree, while Alan goes around the wall on the west.  If both courses are the same distance to the tree, how far were Alan and Bert from the west end of the wall at the start?

The pattern shown is called a “tiling” because it is made up of congruent polygons, fitted together without gaps.  One of these pentagons is enlarged at right.  The pentagon is equilateral, but not regular.  Angles 1 and 2 are right angles, and angles 3 and 4 are congruent.

(Pythagorean Theorem)  Find the height of the pentagon and give it exactly.

(Inverse trig functions)  Find the measures of angles 3, 4, and 5.

(arc length and unit conversion)  How many revolutions per second are the 20-inch diameter wheels of a car turning if the car is moving at 55 mph?  (My students have been weak at unit conversions, which are so fundamental I think they should get such problems in every assignment.)

(angular velocity and unit conversion)  Two cars are driving around a circular track in opposite directions.  The red car has a linear velocity of 45 km/hr and the blue car has an angular velocity of 2.15 degrees per second.  The cars pass each other exactly every 2 minutes.  Find the radius of the track in meters.

(graphing trig functions) A ferris wheel is 40 feet in diameter and its axle is fixed 32 feet above the ground.  Mary got on at time t = 0 seconds into the car at the bottom of the wheel, and as the wheel turned she found it took exactly 48 seconds to go from the bottom point on the circle to the top.  Write an equation h(t) giving Mary’s height above the ground in feet at time t in seconds.

(angular velocity, solving triangles)  When the starship Enterprise entered the Aldebaron system, they found that the star Arcturus had two planets, Bonkus and Conkus.  The radii of their circular, clockwise orbits were 90 million km. and 160 million km. respectively.  A “year” on Bonkus (the amount of time it takes Bonkus to complete one orbit) was 153 days and on Conkus, 870 days.  It so happened that when the Enterprise arrived, the centers of Bonkus and Conkus and the Arcturus were collinear.  Their mission in the Aldebaron system took 39 days.  How far apart were Bonkus and Conkus when the Enterprise departed?

(Headings)  The schooner Elizabeth set off from Allenport at a hearing of 132 degrees, but didn’t return when expected.  After attempts to reach the Elizabeth by radio failed, a rescue boat left Allenport at the same heading to try to find them.  The rescue boat had fuel to go 90 miles, and their plan was to go as far as they could while leaving themselves enough fuel to return to Blake’s Island, which is 26 miles out from Allenport at a heading of 84 degrees.

(Law of cosines)  How far can the rescue boat continue on the 132 degree heading before having to turn back to Blake’s Island?

(Law of sines)  If the rescue boat reaches that point, to what new heading will they turn to proceed straight to Blake’s Island?

Questions, corrections, comments:  Send me e-mail at  markthom@flash.net