To find the angle of elevation of the sun, you can use the tangent function. Given that the shadow of the pole is 2/3 of its length (12 meters), you can set up the following trigonometric relationship:
tan(angle of elevation) = (height of the pole) / (length of the shadow)
tan(angle of elevation) = 12 / (2/3 * 12)
Now, calculate the length of the shadow:
2/3 * 12 = 8 meters
So, tan(angle of elevation) = 12 / 8
tan(angle of elevation) = 3/2
To find the angle of elevation, take the arctan (inverse tangent) of 3/2:
angle of elevation = arctan(3/2)
Using a calculator or trigonometric tables:
angle of elevation ≈ 56.31 degrees
So, the angle of elevation of the sun is approximately 56.31 degrees.