Answer:
The distance of the ship from the cliff is 38.465 feet
The height of the cliff is 46.28 feet.
Step-by-step explanation:
As shown in the figure attached [tex]d[/tex] is the distance from the ship to the cliff, and [tex]h[/tex] is the height of the cliff from the ship.
From trigonometry
[tex]tan(20^o)=\frac{14}{d}[/tex]
[tex]d=\frac{14}{tan(20^o)}=38.465\:feet.\\\\\boxed{d=38.465ft}[/tex]
This is the distance to the cliff.
And we have
[tex]tan(40^o)=\frac{h}{d}[/tex]
since [tex]d=38.465ft[/tex]
[tex]h=d*tan(40^o)=38.465*tan(40^o)=32.28ft[/tex]
Ad the height of the cliff is just [tex]14+h[/tex] or
[tex]32.28+14=46.28 ft\\\\\boxed{height=46.28ft}[/tex]
Which is the height of the cliff.
