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
see the 1st related question below
sin60=10
33
To find the length of the shadow when the angle of elevation of the sun is 45 degrees, we can use trigonometry.
Let's denote the length of the pole as "h" and the length of the shadow as "x".
According to the given information, when the angle of elevation is 60 degrees, the shadow length is 5 meters. This forms a right triangle, where the height of the pole is the opposite side, the length of the shadow is the adjacent side, and the angle of elevation is the angle between them.
Now, we need to find the length of the shadow when the angle of elevation is 45 degrees. This forms another right triangle, but with different values.
Using trigonometry, we can use the tangent function because the tangent of an angle is equal to the ratio of the opposite side to the adjacent side in a right triangle.
For the first scenario (angle of elevation is 60 degrees):
tan(60°) = h / 5
Rearranging the equation, we get:
h = 5 * tan(60°)
Now, for the second scenario (angle of elevation is 45 degrees):
tan(45°) = h / x
We know that h is equal to 5 * tan(60°) from the previous equation. So, substituting the value:
tan(45°) = (5 * tan(60°)) / x
To find the length of the shadow (x), we can rearrange the equation:
x = (5 * tan(60°)) / tan(45°)
Using a calculator to find the values of the trigonometric functions:
tan(60°) ≈ 1.736
tan(45°) ≈ 1
Thus, substituting the values:
x = (5 * 1.736) / 1
x ≈ 8.68 meters
Therefore, the length of the shadow when the angle of elevation is 45 degrees is approximately 8.68 meters.