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.