Question

I hope you are truly going to solve it. Thanks in advance!
In the figure, the point T is the top of a vertical
lighthouse. Boats are moored at the points A, B
and C. The foot, O of the lighthouse, 4, B and C
are all at sea level. The boat at A is 86m from the
point O and the angle of elevation of T from A is
24". The boats at A and B are due east of the
lighthousc'and the distance AB is 40m. The boat a
C is due south of the boat at A and the angle of
elevation of T from Cis 18.
Calculate,
(a) the distance OT, in m to the nearest m,
(b) the distance OB,
(c) the angle of elevation the point T from the boa
at B in degrees to the nearest degree.
Calculate,
(d) the distance CT,
(f) the distance AC,
(g) Calculate, the bearing of the boat at B from the
boat at C, in degrees to the nearest degree.
(e) the distance OC,

Answer 1

Answer:

Refer to Image)

DC=60m

Let height of lighthouse be h metres

In △

le

ABC,tan45

o

=

x

h

⇒x=h .

In △

le

ABD,tan30

o

=

h+60

h

⇒

3

1

=

h+60

h

⇒h+60=

3

h

⇒

3

−1

60

=h

⇒h=

3

−1

60

3

+1

3

+1

⇒30(

3

+1)m .