Question

A man ,1.8 meters tall stands on top of a light house 25 meters high and see a ship at sea at a depression of 35 degree ,How far is it from the foot of the light house

Answer 1

Answer:

Step-by-step explanation:

Given,

Height of light house = 25 m

Height of man = 1.8 m

depression angle = 35 degree

See the below image:

∠ABC = 90° - 35°

          = 55°

We know that,

 tan ∠ABC = $\frac{AC}{AB}$

⇒ tan 55° = $\frac{AC}{AO +OB}$

⇒ tan 55° = $\frac{AC}{25+1.8}$

⇒ tan 55° = $\frac{AC}{26.8}$

⇒ AC = tan 55° × 26.8

⇒ AC = 1.4281 × 26.8

∴ AC = 38.27 m