Roger Q. Haight, lead engineer for Parsons Brinckerhoff, demonstrates the relative strength of square versus triangular struts, with the help of 10th grade volunteer Brandon Otte, during a presentation yesterday.

The Providence Journal / Sandor Bodo

Sophomore Danielle Tremblay assembles a square strut during a demonstration yesterday.

The Providence Journal / Sandor Bodo

NORTH SMITHFIELD — A generation ago, students learned trigonometry because their teachers told them to. At North Smithfield Junior-Senior High School these days, they learn it because, without it, bridges fall down.

It’s a lesson being taught by the school’s mathematics faculty and engineers from international civil engineering giant Parsons Brinckerhoff.

Yesterday morning, about 75 students from North Smithfield Junior-Senior high School geometry and statistics and probability classes gathered to hear a presentation on the fourth annual collaboration between the school and the company in taking trigonometry and other advanced forms of mathematics out of the textbook and into the real world.

One way civil engineers use mathematics is in bridges. Trigonometry lets engineers predict how high and how far they can build a bridge, what it can be made of and how many cars it can carry.

Roger Q. Haight, Parsons Brinckerhoff’s project manager for the Newport-Pell bridge projects, spoke to the students about bridge design and construction and assigned two groups — the geometry and the statistics/probability classes — real-world problems Parsons Brinckerhoff engineers deal with in their jobs.

The students are expected to solve their problems — for the geometry students, designing a truss span and for the statistics students, determining the carrying capacity of a certain mix of concrete being used on a job — as well as present drawings and spreadsheets to back up their conclusions and to submit regular progress reports on how they are doing, just as they would be expected to do in a real engineering firm.

The project ends in the spring with the students traveling to the company’s headquarters in New York City to make a formal presentation of their findings and results to Parsons Brinckerhoff engineers.

Corey S. Brier, a junior who will be participating in his third Parsons Brinckerhoff project, said besides learning how to use trigonometric and advanced mathematical approaches, the program had other beneficial lessons on how to communicate their findings.

“We learn how important it is to make a formal business presentation,” Brier said.

The program started in 2003. It was the brainchild of then-Rhode Island Bridge and Turnpike Authority Director and past North Smithfield Town Administrator Kenneth Bianchi. Bianchi said he had seen a local business-school collaboration and decided to see if he could interest Parsons Brinckerhoff in doing one with North Smithfield.

The company had already worked with a college and a school in New York so it agreed to try it out. The presentation went so well Parsons Brinckerhoff has continued the program.

“Upon reviewing their work, we were impressed with their understanding of trusses and the differences between tension and compression and how to figure area and weights of the members,” Lou Silano and Debbie Moolin wrote in the Parsons Brinckerhoff internal newsletter. “Some students went so far as to use computers for the analysis and employed spread sheets to display their results.”

Janet Pritchard, an associate professor of information systems at Bryant, told the students one of the benefits of the North Smithfield-Parsons Brinckerhoff collaboration was that it took advanced mathematics out of the textbook and the realm of the abstract.

“You get a chance to see how things like mathematics are important,” she said. “It’s a fabulous opportunity for you to see a working environment.”

Daniel O’Brien, a former Town Council vice president who chaperoned one of the trips to New York City, agreed.

“They take something from the classroom, from the textbooks, and they apply it to real life,” he said.

“We collect data, lots and lots of data,” said David Mellor, the mathematics teacher responsible for the classes said. “But more important are the people points. And the people points are all of you.”