Answer:
119.45 m
Step-by-step explanation:
Given:
When angle of elevation of the sun changes from 58° to 36° the length of shadow of a pole increases by 90 m.
To find:
Length of pole = ?
Solution:
Kindly refer to the attached image.
[tex]\triangle ABC[/tex] represents the 1st angle of elevation of sun i.e. 58°
[tex]\triangle ABD[/tex] represents the 2nd angle of elevation of sun i.e. 36°
Change in shadow is represented by CD = 90 m
Let height of pole, AB = [tex]h[/tex] m
Let side BC = [tex]x[/tex] m
Now, let us apply tangent rules in [tex]\triangle ABC, \triangle ABD[/tex] one by one:
[tex]tan\theta = \dfrac{Perpendicular}{Base}\\\Rightarrow tan58^\circ=\dfrac{AB}{BC}\\\Rightarrow tan58^\circ=\dfrac{h}{x}\\\Rightarrow x = 0.624h ..... (1)[/tex]
[tex]tan36^\circ = \dfrac{h}{x+90}[/tex]
Putting value of [tex]x[/tex] using equation (1):
[tex]tan36^\circ = \dfrac{h}{0.624h+90}\\\Rightarrow 0.726\times 0.624h+0.726\times 90 = h\\\Rightarrow h-0.453h =65.34\\\Rightarrow \bold{h = 119.45\ m}[/tex]
119.45 m is the height of pole.
Answer:
119.45 m
Step-by-step explanation
Step-by-step explanation:
Given:
When angle of elevation of the sun changes from 58° to 36° the length of shadow of a pole increases by 90 m.
To find:
Length of pole = ?
Solution:
Kindly refer to the attached image.
represents the 1st angle of elevation of sun i.e. 58°
represents the 2nd angle of elevation of sun i.e. 36°
Change in shadow is represented by CD = 90 m
Let height of pole, AB = m
Let side BC = m
Now, let us apply tangent rules in one by one:
Putting value of using equation (1):
119.45 m is the height of pole.
