Trigonometric functions
posted by Jon on .
Find the value of Sec A. and I have a right triangle BC=30 and BA=34
A)17/8
B)9/17
C)15/17
D)17/15
I chose D

There is missing data here. Is 30 the hypotenuse or one of the legs of the right triangle? The same for 34. There is no way for me to know if BC is one the legs or is BA is the hypotenuse or viceversa.
Once I know that, I can proceed to help you. 
BA is the hypotenuse
BC is the opposite leg 
We use the Pythagorean Theorem to find length AC as step 1. In other words, we MUST find the ADJACENT LEG.
AC^2 + BC^2 = BA^2
AC^2 + (30)^2 = (34)^2
AC^2 900 = 1156
AC^2 = 1156  900
AC^2 = 256
We now take the square root of both sides of the equation to find AC.
sqrt{AC^2} = sqrt{256}
AC = 16
We now have all three sides.
We need secant.
What is secant?
Secant = hypotenuse/adjacent
Well, 34 is our hypotenuse and we just found AC (our adjacent). See it?
Secant = 34/16
The improper fraction 34/16 = 2_1/8 as a mixed number when reduced to the lowest term.
However, 2_1/8 written as an improper fraction is 17/8.
Final Answer: Choice (A)
Done!