本文结合实例,探讨如何构造直角三角形解题.一、计算与求值1.计算线段的长度例1如图1,△ABC中,∠A=15°,∠B=15°,AB=2,求边长AC,BC的长度.分析与思考过点A作BC边上的高AD.构造出直角三角形,转化为对直角三角形的求解.为方便计算,设AC=2x,那么BC=2x,AD=x,DC=3~(1/2)x.由勾股定理,得AD~2+DB~2=AB~2,即有x~2+(2x+3~(1/2)x)~2=2~2,解此方程求出x的值,那么△ABC的边长即可求出. In this paper, with examples, to explore how to construct a right-angle triangle solution. A calculation and evaluation 1. Calculate the length of line segment Example 1 △ ABC, △ A = 15 °, ∠B = 15 °, AB = 2, Seeking the length of the AC, BC. Analysis and thinking over point A for the BC side of the high AD. Constructed right-angled triangle, transformed into a right-angled triangle. To facilitate the calculation, let AC = 2x, then BC = 2x, AD = x, DC = 3 ~ (1/2) x. By the Pythagorean theorem, we have AD ~ 2 + DB ~ 2 = AB ~ 2, ) ~ 2 = 2 ~ 2, solve this equation to find the value of x, then △ ABC side length can be calculated.