Question

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

Answer 1

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.