Question

Two boats approach a lighthouse in the middle of
the sea from opposite directions. The angles of
elevation of the top of the lighthouse from two boats
are a and B. If the distance between the two boats
is x metres, prove that the height of the lighthouse

X

is h=

cota + cotB
()Find h if a 60° B 45 and x = 250 m
(i) Find h if a = 60°, B 30° and x 400 m

Answer 1

Answer:

here is your answer mate

Answer 2

Answer: THE ANSWER IS 3

Step-by-step explanations

Two boats approach a light house in mid-sea from opposite directions. The angles of elevation of the top of the light house from two boats are 30° and 45° respectively. If the distance between two boats is 100 m, find the height of the light house.

Class 10th

RD Sharma - Mathematics

12. Some Application of Trigonometry

Answer :

In the fig AB is the light house of height h (m)

In ∆ABC

tan 30° =

=

x = 100 - √3 h ……………(1)

In ∆ABD

tan 45° =

1=

x = h …………(2)

On substituting value of x from eqn (2) in eqn (1)

h = 100 - √3 h

h + √3 h = 100

h (1 + √3) = 100

h = = ⇒ 50 (√3 - 1)

Therefore height of the light house is 50 (√3 - 1)m

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