Problem:
Triangle ABC has a right angle at C. If sinA=32β, then tanB is
Answer Choices:
A. 53β
B. 35ββ
C. 5β2β
D. 25ββ
E. 35β
Solution:
In the figure, sinA=ABBCβ=32β. So for some x>0, BC=2x,AB=3x and AC=(AB)2β(BC)2β=5βx.
Thus tanB=BCACβ=25ββ.