Given the sample triangle below and the conditions b= square root 7 , c= square root 11, find tan (a)

Assuming that the triangle that we are given is a right triangle. 

Given:

b = √7
c = √11

We can use the Pythagorean theorem to complete the dimensions of the triangle:

c^2  = b^2 + a^2
11 = 7 + a^2
a = 2

Angle A is opposite side a, therefore, 

tan ( A ) = a / c
tan ( A ) = 2 / √11
tan ( A ) = 0.603
tan-1 ( 0.603 ) = A
∠ A = 31.09 degrees

Therefore, the measurement of angle A is 31.09 degrees.