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

answer are

step-by-step explanation:

the largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6   = 0.00000180

1.80 x 10-4   = 0.000180 (bigger, or "less small", than the former one)

so

1.8 x 10-2       = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.