Question

A man standing on the deck of a ship, which is 8m above the water level, observes the angle of elevation of the top of a hill as 60 degree and the angle of depression of the base of the hill as 30 degree. Find the distance of the hill fom the ship and the height of the hill.

Answer 1

$\huge \bf \pink{Hey \: there !! }$


Let AB be the deck and CD be the hill .

Let the man be at B .

Then, AB = 8m .

Let BE $\perp$ CD and AC $\perp$ CD .

Then, $\angle$EBD = 60° and $\angle$EBC = 30° .


•°• $\angle$ACB = $\angle$EBC = 30° .

Let CD = h metres.

Then, CE = AB = 8 m and

ED = ( h - 8 ) m .

From right ∆CAB , we have

$\frac{AC}{AB} = \cot30 \degree = \sqrt{3} . \\ \\ = > \frac{AC}{8 \: m} = \sqrt{3} . \\ \\ = > AC = 8 \sqrt{3} m. \\ \\ = > \therefore BE = AC = 8 \sqrt{3} m.$


From right ∆BED , we have

$\frac{DE}{BE} = \tan60 \degree = \sqrt{3} . \\ \\ = > \frac{h - 8}{8 \sqrt{3} } = \sqrt{3} . \\ \\ = > h - 8 = 8 \sqrt{3} \times \sqrt{3} = 24. \\ \\ = > h = 24 + 8. \\ \\ \huge \boxed{ \blue{ \therefore h = 32.}}$


✔✔ Hence, the distance of the ship from the hill 8√3 metres and the height of the hill is 32 metres ✅✅.



$\huge \red{ \boxed{ \boxed{ \mathbb{THANKS}}}}$



$\huge \bf \blue{ \#BeBrainly.}$

Answer 2

$here \: is \: your \: answer \:$

hey! in this attachment OK......