为了测量河宽,现在岸边选取A,B两点,望对岸的目标C,测定∠CAB=45度,∠CBA=75度,AB=120m,求河宽CD

tan∠CAB = tan45° = 1 ,
可得：AD = CD/tan∠CAB = CD ；
tan∠CBA = tan75° = tan(30°+45°) = (tan30°+tan45°)/(1-tan30°·tan45°) = 2+√3 ,
可得：BD = CD/tan∠CBA = CD/(2+√3) = (2-√3)CD .
CD+(2-√3)CD = AD+BD = AB = 120 ,
可得：CD = 120/(3-√3) = 60+20√3 ,
即：河宽CD为 60+20√3 米.