Answer:
≈ 47.2 m
Step-by-step explanation:
let the height from the sea to the base of lighthouse be h₁
let the height from the sea to the top of the lighthouse be h₂
using the tangent ratio in the right triangle
tan55.1° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{h_{1} }{610}[/tex] ( multiply both sides by 610 )
h₁ = 610 tan55.1°
tan56.5° = [tex]\frac{h_{2} }{610}[/tex] ( multiply both sides by 610 )
h₂ = 610 tan56.5°
then
height of lighthouse = h₂ - h₁
= 610 tan56.5° - 610 tan55.1°
= 610(tan56.5° - tan55.1° )
≈ 47.2 m ( to the nearest tenth )
