測量學試題討論：三角形面積與邊長

Discussion of a Surveying Problem: The Triangle Area and Side

史天元 ； 林宏麟

《地籍測量：中華民國地籍測量學會會刊》 40卷3期 (2021/09) Pp. 1-7

摘要

測量學是一個因應實務需求的學科，在各項數據分析與化算中需要經常性的應用數學，尤其是幾何學。亦因此，在各類測量人員的能力測驗中，相關於幾何學的試題甚為常見。本短文以一題POB測量雜誌所刊登的美國國家工程與測量師考試委員會（National Council of Examiners for Engineering and Surveying, NCEES）試題題解為討論標的。該試題為與面積及邊長相關的幾何類題目，「若已知某三角形三個邊之方向角與其面積時，如何求三角形各邊長」。由於所列解法與台灣一般測量教學時之解法不同，故此討論，以為參考。

並列摘要

Surveying is a profession established for the needs of practical objectives. For the operation and data processing aspects, mathematics is frequently applied, particularly geometry. Consequently, geometry-related problems tend to dominate the various surveying exams such as those for licensure. This note is compiled corresponding to an article published in POB magazine from the United States. The scope of this article is to discuss a sample problem of the National Council of Examiners for Engineering and Surveying (NCEES) for surveying. This problem is related to the area of a triangle: specifically, if the area and the bearing of three sides were known, how to find the length of each side. The solution provided by this article is different from the scheme commonly taught in Taiwanese surveying classes. This note describes and compares the solution schemes.