solution_045a.py

#!/usr/bin/python3
# ===================================================================
# How High is the Mountain
# ===================================================================

from math import radians, sin

# ---- given

flight_altitude  = 14245       # feet
measure_distance = 4100        # distance between measuring points
angle_alpha      = 41          # degrees
angle_beta       = 36          # degrees

angle_gamma = 180 - angle_alpha - angle_beta

alpha_rad = radians(angle_alpha)
beta_rad  = radians(angle_beta)
gamma_rad = radians(angle_gamma)

len_alpha = (sin(alpha_rad) * 4100) / sin(gamma_rad)

vert_dist = sin(beta_rad) * len_alpha

height = 14245 - vert_dist

print()
print(f'The mountain is {round(height)} feet high')
print()