the shadow of an electric pole is 5m long when the angle of elevation of the sun is 60 degree .find the length of the shadow when the angle of elevation of the sun is 45 degree.
height of pole --- h
tan 60 = h/5
h = 5tan60
at 45° ,
tan45 = h/x , where x is the length of the new shadow
x =h/sin45 = 5tan60°/tan45° = ....
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5√3 meters
The length of a pole is measured as 5m to the nearest meter (1) calculate percentage error
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To find the length of the shadow when the angle of elevation of the sun is 45 degrees, we can use the concept of similar triangles.
Let's call the length of the shadow when the angle of elevation is 60 degrees as "L". According to the problem, L is equal to 5m.
Now, let's break down the situation. We have a right triangle formed by the electric pole, its shadow, and the sun's rays. The angle of elevation of the sun is the angle between the ground and the line from the top of the electric pole to the sun.
We can create a similar right triangle when the angle of elevation is 45 degrees. Since the angles are the same, the ratios of the corresponding sides of the two triangles will also be the same.
In both triangles, the opposite side represents the length of the shadow. Therefore, we have a proportion:
L/5 = x/y
Here, x represents the length of the shadow when the angle of elevation is 45 degrees, and y represents the distance from the top of the electric pole to the ground.
We can rearrange the equation to solve for x:
x = (L/5) * y
To find the value of y, we need additional information. Let's assume the distance from the top of the electric pole to the ground is 10m.
Substituting the values into the equation, we have:
x = (5/5) * 10
x = 10m
Therefore, the length of the shadow when the angle of elevation of the sun is 45 degrees is 10m.