Math problem! This is an emergency! ! ! ! ! !

We often say that the slope of the flat roof is 3: 100. 3%

The slope of the gutter is 1.5%, that is, 1.5: 100.

Generally speaking, it is the ratio of slope height to slope bottom.

2.AB is the diameter of the circumscribed circle of the triangle. We can set AB equal to r or 1.

For writing convenience, let AB= 1.

Then, AC= 1*cosA=cosA, BC=sinA, and AD=2.

Obtained by cosine theorem in △BCD

DC & amp； Sup2= sin & ampsup2 A? +? 1? -? 2 Sinakos ∠CBD

= Sin & ampsup2 Answer? +? 1? -? 2 China (-Sina)

= 1? +? 3sin & ampsup2A

Then use cosine theorem to find AD in △ACD, and get

2 & ampsup2cos & ampsup2 answer? +? DC & amp； sup2？ -? 2cosA*DC*cos∠ACD？ (Note: cos∠ACD? =? -sin∠BCD=？ - 1/√ 10)

4? Cos&sup 2 answer? +? ( 1? +? 3sin & ampsup2a)？ -? 2cosA*√( 1？ +? 3sin & ampsup2a)？ ×(- 1/√ 10)

Simplified: 2-2 sin&; Sup2 answer? =2cosA？ √[( 1? +? 3sin & ampsup2A)/ 10]

Solve? :? Sina =3/√ 13

then what tanA=3/2？

The key is to set AB as a fixed value 1, take ∠A as a variable, and then use two cosine theorems to solve sinA.