What is the angle of elevation of the sun when a 47-ft mast casts a 31 ft shadow? Please help!

approximately 57 degrees (when rounded off from 56.59 degrees)

Step-by-step explanation:

Imagine a right triangle with the 90 degree (right) angle at the foot of the mast.  The sun, striking the mast, casts a 31 ft shadow.  Think of this shadow as lying on the "adjacent side" of the angle of elevation, and the height of the mask on the "opposite side."

The trig function "tangent" includes the variables in question:

tan (angle of elevation) = (opposite side) / (adjacent side).

Then, in this particular case,  tan (angle of elevation) = opp side / adj side

takes is

tan (angle of elevation) = 47/31  =  1.516  =  0.9877 radians, or

0.9877 rad      180 deg

*  = 56.59 deg, or approximately 56.6 deg, or

         1               π rad               approximately 57 deg

the transverse axis of a hyperbola is the line that contains the two vertices and the two focuses.

in this example (hyperbola of equation x^2/2 - y^2/4 = 1), the transverse axis is the  x-axis  . 

step-by-step explanation: