Question

In the figure, find the value AB.

Answer 1

LINE OF SIGHT: The line of sight is a line drawn from the eye of an observer to the point in the object viewed by the observer.

ANGLE OF ELEVATION: The angle of elevation of an object viewed is the angle formed by the line of sight with the horizontal , when it is above the horizontal level.

ANGLE OF DEPRESSION:The angle of depression of an object viewed is the angle formed by the line of sight with the horizontal , when it is below the horizontal level.

•Angle of elevation and depression are always acute angles.

•If the observer moves towards the perpendicular line(Tower/ building) then angle of elevation increases and if the observer move away from the perpendicular line(Tower/ building) angle of elevation decreases.

SOLUTION:

Given:
CD = 1000 m, ∠ADC = 60°, ∠BDC= 45°

Let AB = x m , BC = y m

In ∆ADC,
tan 60° = P/B = AC/DC = (AB+BC)/DC
√3 = (x + y) /1000 [tan 60° = √3]
AC(x+y )= 1000√3 m

In ∆BDC,
tan 45° = P/B = BC/DC
1 = y /1000 [tan 45° = 1]
y = 1000

AB = AC - BC
x = AC - y
x = 1000√3 - 1000
x = 1000(√3 - 1) m

Hence, the value of AB is 1000(√3 - 1) m.

HOPE THIS WILL HELP YOU...

Answer 2

Answer:

AC-BC=AB

1000√3-1000

=1000(√3-1)

Step-by-step explanation:

BC=1000 because DC/BC=1

AC=1000√3