A 1.8m tall man casts a 3.12m long shadow. At what angle is the sun to the horizon?

The person stands on the ground at an angle of 90˚. This means that he makes a right angle with his shadow and the line connecting the highest point of the person and the shadow.
In this right triangle, the person is the leg, and the shadow is the other leg.
First, we find the length of the hypotenuse of the triangle by the Pythagorean theorem:
The sum of the squares of the legs is the square of the hypotenuse. Then 1.8² + 3.12² = hypotenuse².
3.24 + 9.734 = 12.94.
The hypotenuse is 3.6, and the ratio of the opposite leg angle to the hypotenuse is the cosine of this angle.
1.8 / 3.6 = 0.5.
And 0.5 is the cosine of the angle, the degree measure of which is 60˚.
ANSWER: the angle that the sun makes with the horizon is 60˚.

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