Sun rays

If the sun's rays are at an angle 60° then famous Great Pyramid of Egypt (which is now high 137.3 meters) has 79.3 m long shadow. Calculate current height of neighboring chefren pyramid whose shadow is measured at the same time 78.8 m and the current height of the nearby Mikerinovi pyramid which at the same time throws a shadow 35.8 m long.

Correct result:

a =  136.4343 m
b =  61.9841 m

Solution:

$$\begin{gathered} h=137.3\text{ m } \\ s=79.3\text{ m } \\ k=h\mathrm{/}s=137.3\mathrm{/}79.3={\displaystyle \frac{1373}{793}}=1\frac{580}{793}\doteq 1.7314 \\ \alpha =180\mathrm{/}\pi \cdot \arctan (h\mathrm{/}s)=180\mathrm{/}3.1416\cdot \arctan (137.3\mathrm{/}79.3)\doteq 59.9907^{\circ } \\ a=k\cdot 78.8=1.7314\cdot 78.8=136.4343\text{ m} \end{gathered}$$

$b=k\cdot 35.8=1.7314\cdot 35.8=61.9841\text{ m}$

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