Question

From a ship masthead 150 ft high, the angle of depression of a boat is observed to be 45 degree
find distance from the ship ​

Answer 1

tan 45= 1

let x be the distance from the ship

tan 45= 150/x

therefore 150/x = 1/1

x = 150 ft

Answer 2

We need to recall the following trigonometric formulas.

• $tan\theta=\frac{Opposite}{Adjacent}$
• $tan45\textdegree=1$

Given:

height of masthead of a ship $=150$ ft

angle of depression $=45\textdegree$

From the triangle $ABC$, we get

$tan45\textdegree=\frac{AB}{BC}$

$1=\frac{150}{BC}$

$BC=150$ ft

Hence, the distance from the ship is $150$ ft.