A man whose eye is 120 m above the ground is standing 8 m from a 7 m tall.What is the angle of elevation of the top of the tree from its eye?
To find the angle of elevation, we can use the tangent function.
First, find the difference in height between the man's eye and the top of the tree:
120 m - 7 m = <<120-7=113>>113 m
Next, use the tangent function. Let θ be the angle of elevation:
tan(θ) = (opposite side) / (adjacent side) = 113 m / 8 m
Now, find the angle by taking the arctangent of both sides:
θ = arctan(113 m / 8 m)
θ ≈ 85.4°
So, the angle of elevation of the top of the tree from the man's eye is approximately 85.4 degrees.