a tree 50m tall casts shadow 60m long .find the angle of elevation of the sun that time
draw a diagram.
tanθ = 50/60
To find the angle of elevation of the sun, we can use trigonometry and the properties of similar triangles.
Let's label the following:
Height of the tree = h = 50m
Length of the shadow = s = 60m
Now, we can set up the proportion between the height of the tree, the length of its shadow, and the angle of elevation:
tan(angle) = h / s
To find the angle of elevation, we need to take the inverse tangent (or arctan) of the ratio h/s:
angle = arctan(h / s)
Substituting the given values:
angle = arctan(50m / 60m)
Using a calculator or reference table, we find:
angle ≈ 0.74 rad ≈ 42.5°
Therefore, the angle of elevation of the sun at that time is approximately 42.5 degrees.