Question

at a certain time, a vertical pole 3 meters tall casts a 4 meter shadow. what is the angle of elevation to the sun? round your answer to the nearest meter.

Answer 1

Your puzzle describes a triangle that has the flagpole standing (OPP)osite the (ANGLE) of elevation, and the shadow forms the (ADJ)acent side.

Because the OPP and ADJ values are given, from the mnemonic SOHCAHTOA, we would choose TOA, which states:

tan(ANGLE) = OPP/ADJ

So with your example:

tan(ANGLE) = 3/4

Now, the inverse of tan(angle) is the angle in "degrees of arc" - which is what you're after.

The inverse of "tan" is called "arctan", and if any given calculator doesn't have an arctan function, you may also use tan^-1, which is the same thing.

So:

degrees of arc = arctan(tan(ANGLE))

which is the same as:

degrees of arc = tan^-1(tan(ANGLE))

or simply:

degrees of arc = arctan(OPP/ADJ)

In your example, that would be:

degrees of arc = tan^-1(3/4)