The shadow of a 60 m long vertical pole is of 10 m. Then what will be the angle of inclination ? Round your answer to the nearest tenth of a degree .
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Answer:
Explanation:
Angles of elevation and depression are always measured from the horizontal.
This means that, at a point at the end of the tree's shadow there is as angle of 60 degrees between the ground and a line to the top of the tree, which is 50m tall.
We assume the tree is vertical, giving a right-angled triangle.
If the length of the shadow is
x
m, then we have the trig ratio using the opposite and the adjacent sides:
50
x
=
tan
60
°
Having the variable in the denominator is not a good idea.
We can change the equation into two different forms:
From
50
x
=
tan
60
°
1
, we can get
x
50
=
1
tan
60
°
Or from
50
x
=
tan
60
°
, we can get
50
=
x
×
tan
60
°
Both of these lead to the calculation for
x
as
x
=
50
tan
60
°
x
=
28.87
m
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