MATHEMATICAL MODELING AND HEIGHT MEASUREMENT: AN EXPERIENCE WITH A THEODOLITE IN HIGH SCHOOL

Abstract

This article aims to demonstrate concretely, through an experimental approach, how trigonometry and mathematical modeling can be applied to measuring the height of a real object, using a theodolite as a support instrument, in a 3rd-year high school class in the city of São Gonçalo do Piauí. The activity was structured in three pedagogical stages: theoretical foundation, practical experience, such as data collection and recording, measurement of elevation angles and horizontal distances, and finally, analysis of the data obtained. The experiment allowed students to empirically observe how to calculate the height of inaccessible objects using information collected in the environment, in addition to understanding the fundamental concepts of trigonometry, with a main focus on the concept of tangent. The results highlight the potential of investigative practice in mathematics teaching, promoting critical analysis skills, data interpretation, problem-solving, and student protagonism, as proposed in the Brazilian National Curriculum Base (BNCC). The proposal reinforces the importance of active methodologies and contextualized pedagogical strategies in the teaching-learning process for teaching fundamental science concepts, favoring the articulation between theory and practice in the school environment.