ABC is a right angled triangle. D is the point on AB such that AD = 3DB. AC = 2DB and angle A = 90 degrees. Show that sinC = k/√20 where k is an integer. Find the value of k
AB = 4DB
AC = 2DB
Find BC using Pythagoras:
BC = √(4DB)2 + (2DB)2
BC = √20DB2
= √20 DB
sinC = opp/hyp = 4DB/√20DB = 4/√20
so k = 4
TJ
