The shadow of an electric pole is 5 m. long when thr angle of elevation of the seen is 60 degrees. Find the length of the shadow when the angle of elevation of the seen is 45 degrees
clearly the pole has height 5√3. (since tan 60 = √3)
That will be the length of the shadow also when the angle is 45 degrees.
To find the length of the shadow when the angle of elevation of the sun is 45 degrees, we can use trigonometric ratios.
Let's assume the height of the electric pole is H m and the length of the shadow when the angle of elevation is 60 degrees is S m.
Using the tangent function, we can write:
tan(60°) = H/S
Rearranging the equation, we get:
S = H/tan(60°) -------- (Equation 1)
Now, we need to find the length of the shadow when the angle of elevation is 45 degrees. Let's call this length X m.
Using the tangent function again, we can write:
tan(45°) = H/X
Rearranging the equation, we get:
X = H/tan(45°) -------- (Equation 2)
To find the value of X, we need to substitute the value of H from Equation 1 into Equation 2:
X = (H/tan(45°)) = (H/1) = H
Since the height of the electric pole remains the same, the length of the shadow when the angle of elevation is 45 degrees would also be H meters.
Therefore, the length of the shadow when the angle of elevation is 45 degrees is the same as the height of the electric pole.
To find the length of the shadow when the angle of elevation of the sun is 45 degrees, you can use trigonometry.
Let's assume the height of the electric pole is 'h' meters.
When the angle of elevation is 60 degrees, we can form a right triangle with the height of the pole as the opposite side and the length of the shadow as the adjacent side. We can now use the tangent function:
tan(60 degrees) = opposite/adjacent
tan(60 degrees) = h/5
√3 = h/5
h = 5√3 meters
Now, we can find the length of the shadow when the angle of elevation is 45 degrees. Again, we can form a right triangle with the height of the pole as the opposite side and the length of the shadow as the adjacent side. We can use the tangent function again:
tan(45 degrees) = opposite/adjacent
tan(45 degrees) = 5√3 / x (let x be the length of the shadow)
1 = 5√3 / x
x = 5√3
Therefore, the length of the shadow when the angle of elevation of the sun is 45 degrees is 5√3 meters.