Question

Suppose that x is an acute angle of a right triangle and that tan(x)=(3 square root 2)/(8). Find sec(x) and csc (x).

Answer 1

Tan is opp/ adj therefore, opposite = 3root2 and adj= 8.
To find the hyp. use a^2 +b^2 = c^2 to find that hyp = root70
You're looking for sec which is hyp/adj or root70/8
and csc which is hyp/opp or root70/3root2

Answer 2

find the hypotenuse using pythagoras. then use the trig ratios
secant is hypotenuse over adjacent, cosecant it hypotenuse over opposite

Answer 3

hypotenuse is
\[\sqrt{8^2+(3\sqrt{2})^2}\]
\[=\sqrt{64+18}=\sqrt{82}\]