In the triangle ABC shown below (not to scale): tanA=1/6 and tanB 2/3

M is the midpoint of AB.

What is the value of tan θ

Answer:

16) C

This is a tricky question.

First, draw a line perpendicular to AB from C. Label the line be CP.

We have tan A = CP = 1
AP 6

So, CP = 1, AP = 6

We have tan B = CP = 2
BP 3

Since CP = 1, BP = (3 ÷ 2) = 1.5

Since BP = 1.5, then AP = 6

AB = (AP + BP) = (1.5 + 6) = 7.5

Since M is the mid point, BM = (7.5 ÷ 2) = 3.75

PM = (BM – BP) = (3.75 – 1.5) = 2.25

tanθ = CP
PM

CP = 1
PM 2.25

1 = 4

2. 25 9