Final answer:
To find the height of the pyramid, we can use trigonometry and the tangent function. By setting up two equations using the angles of elevation and the distances between the points, we can solve for the height.
Step-by-step explanation:
To find the height of the pyramid, we can use trigonometry. Let's assume that the point on the ground is A and the point 176 feet farther back is B. The angle of elevation from A to the top of the pyramid is 30°10', and the angle of elevation from B to the top of the pyramid is 20°30'. We can use the tangent function to calculate the height of the pyramid.
From point A, we have:
tan(30°10') = height of the pyramid / AC
From point B, we have:
tan(20°30') = height of the pyramid / BC
Since AC = BC + 176 feet, we can substitute AC - 176 for BC in the second equation:
tan(20°30') = height of the pyramid / (AC - 176)
Now, we can solve these two equations simultaneously to find the height of the pyramid.