Algebra and Trig question. Please show work! Serious replies only!! I really do appreciate the help?

Question

If cos 0 = 5 /8, find tan 0

a). 8 square root 39 over 39
b). square root 39 over 5
c). 5 square root 30 over 39
d). square root 39 over 8

Answer 1

Cos angle = side adjacent / hypotenuse

Therefore side adjacent = 5, and hypotenuse = 8 of a right triangle.

Using the Pythagorean theorem.
8^2 = (side opposite)^2 + 5^2
(side opposite)^2 = 64 - 25 = 39
side opposite = (39)^0.5

Tan angle = side opposite / side adjacent

Therefore

Tan angle = (39)^0.5/5 = Square root 39 over 5
.

Answer 2

It is C because i did it on my calculator.