a gril of height 90 cms is walking away from the base of a lamp post at a speed of 1.2m/sec.If the lamp post is 3.6m above the ground, find the length of her shadow after 4 seconds?
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Let the girl Rita of height be at point D on the ground from the lamp post after 4 sec.
∴ AD = 1.2 m/sec × 4 sec = 4.8 m = 480 cm
Suppose the length of the shadow of the girl be x cm when she at position D.
∴ BD = x cm
In ∆BDE and ∆BAC
∠BDE = ∠BAC (90°)
∠DBE = ∠ABC (Common)
∴ ∆BDE ∼ ∆BAC (AA similarity)
BE / BC = DE / AC = BD / AB ( Cooressponding angles are proportional )
90 / 360 = x / (480 + x)
1 / 4 = x / (480 + x)
4x = 480 + x
x = 480 / 3 = 160
∴ Length of Rita shadow after 4 second is 160 cm.
∴ AD = 1.2 m/sec × 4 sec = 4.8 m = 480 cm
Suppose the length of the shadow of the girl be x cm when she at position D.
∴ BD = x cm
In ∆BDE and ∆BAC
∠BDE = ∠BAC (90°)
∠DBE = ∠ABC (Common)
∴ ∆BDE ∼ ∆BAC (AA similarity)
BE / BC = DE / AC = BD / AB ( Cooressponding angles are proportional )
90 / 360 = x / (480 + x)
1 / 4 = x / (480 + x)
4x = 480 + x
x = 480 / 3 = 160
∴ Length of Rita shadow after 4 second is 160 cm.
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