Questions: A pyramid was built about 2580 BC. Its original height was 411 feet, 5 inches, but due to loss of its topmost stones, it is now shorter. Find the current height of the pyramid, using the information given in the figure. The current height of the pyramid is feet. (Do not round until the final answer. Then round to two decimal places as needed.)

Solution Steps

Let $h$ be the total height of the larger triangle. We are given the base of the larger triangle is 250 ft and the angle opposite the height is $39.1^\circ$. We can use the tangent function to relate the height and base of the triangle: $\tan(39.1^\circ) = \frac{h}{250}$ $h = 250 \times \tan(39.1^\circ)$ $h \approx 203.73$ ft

Let $x$ be the height of the smaller triangle (shaded yellow). We are given the base of the smaller triangle is 125 ft and the angle opposite the height is $48.09^\circ$. We can use the tangent function to relate the height and base of the triangle:

$\tan(48.09^\circ) = \frac{x}{125}$

$x = 125 \times \tan(48.09^\circ)$

$x \approx 139.75$ ft

The current height is the difference between the total height and the height difference. Current height $= h - x$ Current height $= 203.73 - 139.75 = 63.98$ ft

Final Answer: The final answer is $\boxed{63.98}$