Mr. Banta observing from the top of the light house finds that Boat A and Boat B are approaching to
light house from the opposite directions. He finds that the angle of depression of the Boat A is 450
and angle of depression of Boat B is 300
. He also is aware of the height of the light house is 100m.
Answer the following question:
(i) Find ABC
(a) 300
(b) 450
(c) 600
(d) none of these
(ii) What was the base BC?
(a) 40 m
(b) 60 m
(c) 100 m
(d) 45 m
(iii) Give the reason for ADB= 300
(a) Interior angles on the same side of the
(b) Vertically Opposite angles
(c) Alternate interior angles
(d) None of these.
(iv) What is the length of BD
(a) 100m
(b) 50
(c) 100√3
(d) 100√2
(v) Find the distance AC
(a) 100√3 m
(b) 50√3 m
(c) 100√2 m
(d) 50√2 m
Answers
Answer:
question answer is a 200-300 is the second question answer sexy metres short question answer is opposite angles question answer is 100
Root 2 metres
Given :
Correct Question should be:
boat A and boat B are approaching the light house from the opposite directions,
angle of depression of boat A is 45 degree and the angle of depression of boat B is 30 degree
height of the light house is 100m
To Find : Distance between Boats
Angle ABC
BC
Give the reason for ∠ADB= 30°
Solution:
Angle ABC = 45° ( alternate interior angle)
Tan 45° = 100/BC
=> BC = 100 m
∠ADB= 30° Alternate interior angles
Height of light House = 100 m
angle of depression of boat A is 45°
Angle of elevation = angle of depression
Tan 45° = 100 / Horizontal distance of Boat A
=> 1 = 100 / Horizontal distance of Boat A
=> Horizontal distance of Boat A = 100 m
angle of depression of boat B is 30°
Tan 30° = 100 / Horizontal distance of Boat B
=> 1/√3= 100 / Horizontal distance of Boat B
=> Horizontal distance of Boat B = 100√3 m
Distance between Boats = 100 + 100√3 m
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