Geometry easy??? 10 points.?

Question

If the cos of an angle is .75, what is the csc?

Answer 1

It would help to be able to draw a diagram, but...

If the cos (A) = .75  (I prefer (3/4),

then the side adjacent = 3 and the hypotenuse = 4

(at least, they are in that ratio.  This is true by the definition of COS.)

Solve for the third side (opposite side to angle A):

3^2 + a^2 = 4^2 = 16

a^2 = 7

a = sqrt 7

The csc (A) = (hypotenuse)/(side opposite) = 4/(sqrt 7)

Rationalize:  

csc (A) = 4(sqrt 7)/7

A very ugly triangle!