A boy 1.4m tall stood 10m away from a tree of height 12m .calculate and correct to the degree and the angle of elevation
The angle of elevation can be found using the tangent of the angle, which is the ratio of the opposite side (height of the tree - height of the boy) to the adjacent side (distance from the tree).
Height difference = 12m - 1.4m = 10.6m
Opposite Side = 10.6m (Vertical height difference)
Adjacent Side = 10m (Horizontal distance)
So, tan(θ) = Opposite Side / Adjacent Side
= 10.6 / 10
= 1.06
To find the angle, we use the inverse tangent function:
θ = tan^(-1)(1.06)
Using a calculator,
θ ≈ 46.43 degrees. So, the angle of elevation, to the nearest degree, is approximately 46 degrees.
To calculate the angle of elevation, which is the angle between the ground and the line of sight from the boy to the top of the tree, we can use the tangent function.
Let's assume that the angle of elevation is denoted by θ.
First, we need to find the distance between the boy and the top of the tree. This can be calculated using the Pythagorean theorem:
Distance^2 = Height^2 + Distance^2
Distance^2 = 12^2 + 10^2
Distance^2 = 144 + 100
Distance^2 = 244
Distance = sqrt(244)
Distance ≈ 15.62m
Now, we can use the tangent function to find the angle of elevation:
tan(θ) = opposite/adjacent
tan(θ) = Height/Distance
tan(θ) = 12/15.62
θ = atan(12/15.62)
Using a calculator, we can calculate the angle:
θ ≈ 38.91 degrees
Therefore, the angle of elevation is approximately 38.91 degrees.