Law of Sines - Triangle Lab

Students need to learn that great care needs to be taken in measuring the angle to have accurate estimates.

Here students are measuring an acute triangle created by running a rope up and over an emergency shower head. Both ends are taped to the floor. Distance measurements are only allowed along the floor. The sketch below demonstrates that the two angles and the distance along the floor should be measured. Additionally, students are asked to find the height of the object the rope passes over.

The complex system shown below requires two measurements to be taken at this vertex.

The sketch above denotes the instructions posted at each station instructing the students which measurements to make. The angle at the counter top below is the only measurement they are allowed to make which is not on the floor.

The enhanced image above shows the triangle with one vertice at the floor, one vertice on the counter top and the final vertice at the ceiling. Students measure the distance along the floor and determine the angle at the countertop as well as both angles at the floor. This activity requires the use of right triangle trigonometry and the law of sines.

The final triangle depicted in the image below has two strings attached to the floor and reaching to the top of the bulletin board. Students are asked to measure angles A and B along with the length of side c along the floor. Besides solving the triangle, students must find the height of the bulletin board at the top vertice of the triangle.