高考数学：解三角形
A high-school mathematics practice set on solving triangles: the law of sines, the law of cosines, triangle area formulas, and angle-side relationships.
- Apply the law of cosines to find a missing side given two sides and the included angle
- Apply the law of sines to find the circumradius of a triangle
- Determine the number of triangles satisfying given side and angle conditions
- Use the Pythagorean converse to identify a right triangle from its side lengths
高考数学：解三角形专题训练；题目自包含、答案可验证。
示例问题
在 $\triangle ABC$ 中，若 $a=3, b=5, C=120^\circ$，则边 $c$ 的长度为多少？
- $5$
- $6$
- $7$
- $8$
查看答案
$7$
根据余弦定理 $c^2 = a^2 + b^2 - 2ab \cos C$，代入数据得 $c^2 = 3^2 + 5^2 - 2 \cdot 3 \cdot 5 \cdot \cos(120^\circ) = 9 + 25 - 30 \cdot (-0.5) = 34 + 15 = 49$，故 $c=7$。