A street light bulb is fixed on a pole of 6m above the level of the street . If a women of height 1.5m casts a shadow of 3m . Find how far she is away from the base of the pole ?
Answers
Answer:
The answer will be 9m.
Step-by-step explanation:
We have given;
Height of pole = 6m;
Height of woman = 1.5m;
Length of her shadow = 3m;
The angle formed between the ray of light and the shadow top will be equal for both the lady and the lamp.
Let θ be the angle formed between the ray of light and the lady's shadow top.
Hence, Tanθ = Lady's height / Her shadow height; (Tanθ = perpendicular / base and here, perpendicular is the lady's height and base is her shadow's height.)
Thus, Tanθ = 1.5m / 3m;
= 1/2; (i)
Tanθ will be same for the lamp.
Hence, Tanθ = Height of the lamp / (lady's distance from lamp base + her shadow height)
here, let her distance from the lamp base be x.
Thus, Tanθ = 6 / (x + 3)
1/2 = 6 /(x+3) (from equation (i) and Tanθ is equal for both the cases)
x + 3 = 12;
x= 9m.
That's all.