Question

World problem in length (trigonometry) geometry not chemistry

Answer 1

≈ 47.2 m

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° =
`(opposite)/(adjacent)` =
`(h_(1) )/(610)` ( multiply both sides by 610 )

h₁ = 610 tan55.1°

tan56.5° =
`(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 )