what is the width to the Nile river in this question

Question

the annual flooding of the Nile river was an important part of the life for the ancient Egyptians.imagine that you must determine that width of the Nile at its crest near the great pyramid. you know the distance from the edge of the pyramid to the near bank is 1 km, and that you are 3.5 km from the opposite bank. from where you are standing, the angle of elevation to the pyramid's peak is approximately 1.5*.

Answer 1

Considering the hight of the pyramid "h" and the base "b" then:

tan(1.5^o) = h / L where

L = b/2 + 1km + x + 3.5 km, where x is width of Nile;

L = h cot(1.5^o) = b/2 + x + 4,5 km;

x = h cot(1.5^o) - b/2 - 4.5 km;

using known data for the Great Pyramid of Giza: h = 146.6 m; b = 230.6 m;

x = 146.6 cot(1.5^o) - 115.3 - 4,500

x = 5,598.43 - 4,4615.3 = 983.13 m

x = 0.983 km