Question

24m
12m
4m
2m

A 24 m high lighthouse casts a shadow of 8m and a ship next to the lighthouse casts a shadow of 4 m.
Find the height of the ship
​

Answer 1

Answer:

the high of the ship is 48

Answer 2

Answer:

The correct answer for the ship's height is found to be option (ii): 12m

Step-by-step explanation:

The lighthouse's height is given to us as: 24m

The length of the shadow cast by the lighthouse is: 8m

A right angled triangle will be formed with the perpendicular being 24m and base being 8m. Using the trigonometric tangent function in the resulting triangle, we get:

$tan(\theta)=\frac{perpendicular}{base}$,

where $\theta$ is the angle of depression from the top of lighthouse to ground level.

Substituting the values, we get:

$tan(\theta)=\frac{24}{8}$                               ...(i)

Now, for finding the height of the ship, the angle of depression will be the same and the base will be the length of the shadow of ship.

Let the height of the ship be $x$, the expression becomes:

$tan(\theta)=\frac{x}{4}$                               ...(ii)

Equating (i) and (ii) as $\theta$ is the same in both equations, we get:

$\frac{24}{8}=\frac{x}{4}$

Using cross multiplication, we get:

$x=\frac{24}{8} \times4$

Or we can say:

$x=12\ m$

So, the height of the ship is found to be 12m.