The use of triangle: Guangdong Paper Mathematics 18 in 2022 College Entrance Examination.

The opposite sides of the inner corner of the paper money are known respectively.

(1) If, ask;

(2) the minimum value;

Answer the question 1

* ∴and

∴ .

Answer question 2

∵ ,

∴

∴ .

In the middle again,,,

Once again: Ⅷ

According to sine theorem,

∵

When the equal sign is established.

The minimum value of ∴ is.

Refine and improve

This topic has two characteristics. First of all, it needs a higher trigonometric identity transformation. The second is to integrate the investigation of inequality into the triangle problem.

In recent years, the requirements of trigonometric identity transformation in high school textbooks and college entrance examination questions have decreased. This practice will cause hidden dangers to students' study in college.

As the baton of high school teaching, it is a correct change to improve the requirements of trigonometric identity transformation in college entrance examination mathematics.

Combining trigonometry with inequality is a long-standing practice, which is not new.