Homework Help

Trigonometry question???A person sitting on a boat is situated 2 metres above sea...

user profile pic

nerdygirl-1996 | Student, Undergraduate | Honors

Posted July 16, 2012 at 7:23 AM via web

dislike 1 like

Trigonometry question???

A person sitting on a boat is situated 2 metres above sea level. He has a device for measuring angles and notes that a straightline from himself to the top most point of a nearby lighthouse makes an angle of 16 degrees wuth the horizontal. After travelling a further 50m from the lighthouse this angle has decreased to 12 degrees. 

How high is the top most point of the lighthouse above sea level (asssuming no triangles are right angled)?

1 Answer | Add Yours

user profile pic

jeew-m | College Teacher | (Level 1) Educator Emeritus

Posted July 16, 2012 at 7:19 PM (Answer #1)

dislike 1 like

Let the height of light house above the the sitting man is x meters. Then the height of light house above sea level = x+2

The horizontal distance between ligh house and man = y

So for first angle;

tan (16) = x/y----------------(1)

For second angle;

tan (12) = x/(y+50)------------(2)

 

(1)/(2) gives

tan (16)/tan (12) = (x/y)/(x/(y+50)

      0.287/0.213  = (y+50)/y

By solving this you can get y = 143.2 m

Form (1)   tan (16) = x/y

                   0.287 = x/143.2

                         x = 41.06

 

Then the height of light house;

= x+2

= 41.06+2

= 43.02m

 

Assumption

The horizontal line of sight of the man is 2m above sea level.

 

                 

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes