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.