In the triangle ABC, 1. If ∠ C = 90, cosa = 12 / 13, find the value of SINB. 2. If ∠ a = 35, B = 65, try to compare the size of cosa and SINB If this triangle is an arbitrary acute triangle, can we judge the size of cosa + CoSb + COSC and Sina + SINB + sinc There is no graph

In the triangle ABC, 1. If ∠ C = 90, cosa = 12 / 13, find the value of SINB. 2. If ∠ a = 35, B = 65, try to compare the size of cosa and SINB If this triangle is an arbitrary acute triangle, can we judge the size of cosa + CoSb + COSC and Sina + SINB + sinc There is no graph


Let ABC be a triangle, ∵ ∠ C = 90 °,
Cosa = 12 / 13, let AC = 12t, ab = 13T,
∴BC=√[(13t)²-(12t)²]=5t,
∴sinB=5/13.
From a / Sina = B / SINB,
∵sinA<sinB,∴a<b.



As shown in the figure, the points E and F are BF = CE, ab = DC, AE = DF on BC, and the verification is ∠ a = ∠ D


Because BF equals CE, be equals FC (equality property)
Because AE is parallel to KD, the angle AEF is equal to the angle DFC
Because AE is equal to FD, the triangle Abe is equal to the triangle DCF
So AB is equal to CD
Because BF is equal to CE, FD is equal to AE, and BFD is equal to AEC, so BFD is equal to CEA, so
AC equals BD, and ab equals DC
So the quadrilateral ABCD is a parallelogram, so AB is parallel to CD
I'm sorry, I use apple. It's hard to type in capitals. Please forgive me!



As shown in the figure, ab = CD, AE ⊥ BC, DF ⊥ BC, CE = BF


It is proved that: ∵ AE ⊥ BC, DF ⊥ BC, ∵ DFC = ∠ AEB = 90 ° and ∵ CE = BF, ∵ ce-ef = bf-ef, that is, CF = be, ∵ AB = CD, ≌ RT △ DFC ≌ RT △ AEB (HL), ≌ AE = DF