Here we can use the formula

$$\begin{gathered} \text{Average (A)=}\frac{\mathrm{Sum} \mathrm{of} \mathrm{observations} \left(\mathrm{S}\right)}{\mathrm{No}. \mathrm{of} \mathrm{observations} \left(\mathrm{N}\right)} \\ \text{⇒ S=A×N} \end{gathered}$$

According to the question,

Sum of height of 16 students (A=142, N=16)

⇒S=142 X 16 =2272

Later, the height of the teacher included, the average height increases by 1 cm. (so A=143, N=17)

So, sum of height of 16 students and a teacher

⇒S=143 X 17 =2431

Now,

Height of the teacher =(sum of height of 16 students)-(Sum of height of 16 students and a teacher)

=2431-2272

= 159 cm.

Hence, Option B is correct.