Question

World problem in length (trigonometry) geometry not chemistry

Answer 1

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° = $\frac{opposite}{adjacent}$ = $\frac{h_{1} }{610}$ ( multiply both sides by 610 )

h₁ = 610 tan55.1°

tan56.5° = $\frac{h_{2} }{610}$ ( 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 )