Find the angle elevation of the top of the tree 13m high from a point 25m away on ground level

Question

I need a lot of help with my worksheet for math. Please anybody help me I have a lot of questions that need to be answered

Answer 1

Think of the tree and the and the point 25m away forming two sides of a triangle. The point they meet is a right angle, or 90 degree angle. To obtain the angle use the fact that the tangent of an angle is the opposite side divided by the adjacent side of the triangle. So if the angle in question here is x then tan x = 25/13. To solve for x,  x = arctan(25/13) = 62.5 deg.

Answer 2

Hi,
Angle of elevation is the angle between observer's eye (horizontal line of reference) and top of object at observer's line of sight (tree in this case).

Height of tree=y=13m
Horizontal Distance between point of observation and object= x=25
Angle of elevation=θ=?

 

Consider a right angled triangle formed with vertical side as height of tree (y) and horizontal side as observation distance (x). Angle θ is the acute angle formed which can be found using trigonometric function i.e. tanθ.

Solution:

tanθ = y/x = 13/25=0.52

θ=tan(inverse) of (0.52)

θ=27.47º which is the required angle of elevation

 

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