Question

In a ship of length $28m$, height of its most is $12m$ if the height of the most in its mood $9cm$ what is the length of the model ship?

• A. $31$ cm
• B. $41$ cm
• C. $21$ cm
• D. $11$ cm

Answer 1

Answer: (D)

$11$ cm

A mast is located a exact center of a ship

In ${\Delta }^{le}ABC$

$\tan \theta =\frac{AB}{BC}=\frac{12}{14}$

$\Rightarrow \theta ={\tan }^{-1}\left(\frac{12}{14}\right)={40.601}^o$

$\theta$ will be same for model ship too:

$\Rightarrow \tan \theta =\frac{\text{Height of mast of model ship}}{\text{length of model ship}}$

$\tan \left(40.601\right)=\frac{9cm}{L}$

$L=\frac{9}{\tan \left(40.601\right)}$

$\Rightarrow L=10.5cm\approx 11cm$