CÓMO CALCULAR LA ALTURA DE UN ÁRBOL CON TRIGONOMETRÍA

CÓMO CALCULAR LA ALTURA DE UN ÁRBOL CON TRIGONOMETRÍA

by Matemáticas con Juan

Formal & Physical Sciences Mathematics PBMGeometryPBMBTrigonometry
🎙 Matemáticas con Juan 👥 2.1M 📅 July 28, 2026 ⏱ 17 min 👁 6K 📄 tutorial 🧭 2026-08-06
Available in: English (current) Français

Keywords

trigonometrytree heighttangentrationalizationequation solving

Summary

The video presents a classic trigonometry problem: calculating the height of a tree using two observation angles (30° and 45°) and a known horizontal distance of 4 meters. The instructor first reviews the fundamental trigonometric ratios (sine, cosine, tangent) in a right triangle. He then identifies two right triangles formed by the tree and the observer, introducing variables x (horizontal distance) and h (tree height). Applying the tangent function to each triangle yields two equations: tan(30°) = h/(x+4) and tan(45°) = h/x. Since tan(45°) = 1, it follows that h = x. Substituting this into the first equation and solving step by step, he derives the exact expression h = 4√3/(3−√3). He then rationalizes the denominator by multiplying by the conjugate, simplifies using algebraic identities, and obtains the simplified exact result h = 2√3 + 2 meters, approximately 5.46 meters. The solution integrates trigonometry, algebra, equation solving, factoring, and rationalization, making it a comprehensive exercise. The video concludes with a proposed problem for viewers to practice.

166 words

Critical Evaluation

The video is an excellent educational resource for learning how to apply trigonometry to real-world problems. The instructor’s approach is methodical and clear, ensuring that viewers understand each step. He begins by defining the essential trigonometric ratios, which is crucial for beginners. The problem is well-chosen as it requires the use of two right triangles and the tangent function, leading to a system of equations. The algebraic manipulation is thorough, including substitution, solving for the unknown, and rationalizing the denominator. The final result is presented both in exact form and as a decimal approximation. The explanation is rigorous and mathematically correct. The instructor also emphasizes the importance of avoiding haste and shows a passion for the subject. The video is well-structured with chapters, making it easy to navigate. The only minor critique is that the video could have included a brief discussion on the practical applications of such calculations, but this is not a significant flaw. Overall, the content is highly reliable and pedagogically effective.

165 words

Title / Content Match

The title accurately reflects the content: the video demonstrates how to calculate a tree's height using trigonometry.

Quality & Reliability

9/10

The video provides a rigorous, step-by-step mathematical derivation of the tree height using trigonometric ratios and algebraic manipulation. The reasoning is clear, accurate, and well-structured, with proper definitions and justifications. The final result is correctly derived and rationalized. The channel is dedicated to mathematics education and the presentation is pedagogically sound.

Chapters

Cited Sources

Concurring Sources

  • Trigonometry — General reference for trigonometric concepts, consistent with the video's content.

Contribution & Novelties

The video provides a clear, step-by-step solution to a classic trigonometry problem, integrating multiple mathematical concepts. Its originality lies in the pedagogical approach, emphasizing the process of rationalization and algebraic simplification. The problem is presented in a real-world context, making it relatable and engaging.

Pour aller plus loin :

82 words

Radar Profile

The radar profile shows high scores in quality and reliability, with slightly lower but still good scores in quantity and technical level. This indicates a well-crafted educational video that balances depth and accessibility.

Reliability 9/10