Sun rays

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

Final Answer:

a =  136.4343 m
b =  61.9841 m

Step-by-step explanation:

$$\begin{gathered} h=137.3\text{m} \\ s=79.3\text{m} \\ A=78.8\text{m} \\ B=35.8\text{m} \\ k=h/s=137.3/79.3=\frac{1373}{793}\doteq 1.7314 \\ k=\tan \alpha \\ \alpha =\frac{180°}{\pi }\cdot \arctan k=\frac{180°}{\pi }\cdot \arctan 1.7314\doteq 59.9907{}^{\circ } \\ \alpha \doteq 60{}^{\circ } \\ a=k\cdot A=1.7314\cdot 78.8=136.4343\text{m} \end{gathered}$$

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

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