Çözüldü Pythagorean Theorem, Percentage, and Factorization Problem (8th Grade)

For the 8th grade test exam, the use of a calculator is permitted:

Assuming a perfectly spherical Earth with a mean radius of 6,371 kilometers, and atmospheric refraction bends light slightly along the curvature of the Earth by effectively extending the visual horizon up to 10%, how far can the maximum visible horizon increase on a perfectly clear day for a person in an airplane flying at an altitude of 700 meters?

A) 102
B) 104
C) 106
D) 108
E) 110


https://i.ibb.co/nNLznXwD/horizon.png

(6371 + 0.7)^2 = 6371^2 + d^2
(6371 + 0.7)^2 - 6371^2 = d^2
(6371 + 0.7 + 6371)(6371 + 0.7 - 6371) = d^2
(12742.7·0.7)^0.5 = d
√(8919.88) = d
94.45 km ≈ d
Maximum Visible Horizon = 94.45·1.1 = 103.889 ≈ 104 km.

Explanation by Google Gemini:

https://i.ibb.co/VrtzsfK/horizon-Gemini.png

Source (Turkish):
"Fizik - Cilt I, Mekanik ve Isı", Prof.Dr. Erich Hausmann, New York University Tandon School of Engineering (formerly Brooklyn Polytechnic Institute), Prof.Dr. Edgar Slack, (aynı üniversite)
Çeviren: Prof.Dr. Nusret Kürkçüoğlu, İTÜ, Eylül 1974, Matbaa Teknisyenleri Basımevi, Sayfa 11, Problem 7'nin Google Gemini katkısıyla biraz zorlaştırılmış şekli