Prosím, vyriešte q 95?

odpoveď:

Dĺžka najdlhšej strany je #21#.

vysvetlenie:

V # # DeltaABC, # RarrcosA = (b ^ 2 + c ^ 2 a ^ 2) / (2BC) #

# RarrArea = (1/2) a * bsinC #

teraz, # # Area z # DeltaABD = (1/2) * 9 * 8 * sinx = 36sinx #

# # Area z # DeltaADC = (1/2) * 8 * 18 * sinx = 72sinx #

# # Area z # DeltaABC = (1/2) * 9 * 18 * sin2x = 81sin2x #

# RarrDeltaABC = DeltaABD + DeltaADC #

# Rarr81sin2x = 36 * sinx + 72 * sinx = 108 * sinx #

# Rarr81 * 2cancel (sinx) * cosx = 108 * zrušiť (sinx) #

# Rarrcosx = (108) / 162 = 2/3 #

Uplatňovanie kosínus práva v # # DeltaABC, dostaneme, # Rarrcos2x = (9 ^ 2 + 18 ^ 2 a ^ 2) / (2 * 9 * 18), #

# Rarr2cos ^ 2x-1 = (405-a ^ 2) / 324 #

# Rarr2 * (2/3) ^ 2-1 = (405-a ^ 2) / 324 #

# Rarr2 * (4/9) -1 = (405-a ^ 2) / 324 #

# Rarr-36 = 405-A ^ 2 #

# Rarr ^ 2 = 405 + 36 = 441 #

# Rarr = 21 #

tiež poznač si to

# Rarrsin2x = 2sinxcosx #

# Rarrcos2x = 2cos ^ 2x-1 #