SOLUTION: A five-foot sophomore at D-E casts an eight-foot shadow. How high is the Sun in the sky? This question is not asking for a distance, by the way. I found the hypotenuse of the tr

Question 1190383: A five-foot sophomore at D-E casts an eight-foot shadow. How high is the Sun in the sky? This question is not asking for a distance, by the way.
I found the hypotenuse of the triangle and I'm not sure where to proceed. I have also done tan of 5/8 which gets me 0.625, but I still have no idea for how to do this.
Answer by math_tutor2020(3816) (Show Source): You can put this solution on YOUR website!

tan(angle) = opposite/adjacent
tan(angle) = 5/8
tan(angle) = 0.625
angle = arctan(0.625) .... same as inverse tangent i.e.

angle = 32.00538

The angular height is roughly 32.00538 degrees above the horizontal
This is the angle of elevation.

Extra info:
An angular height of 0 degrees means the sun is at the horizon (sunrise or sunset)
An angular height of 90 degrees means it is 12:00 PM noon.

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