Question

Stephan is standing on the ground by a mesa in the painted desert. stephan is 1.8 meters tall and sights the top of the mesa at 29 degrees. stephan steps back 100 meters and sights the top at 25 degrees. how tall is the mesa

Answer 1

Angle of sight from point A to tip of Mesa= 29 degrees
Angle of sight at point B to tip of Mesa = 25 degrees
Distance between A and B = 100 m
Let's height of Mesa from sight point be h and height of Stephen is 1.8 m.
With the point A traingle, h is derived as h = b x tan 29, b being the base.
With the point B traingle, h is derived as h = (b +100) x tan 25, b being the base
So b x tan 29 = (b +100) x tan 25 => (b x tan 29) - (b x tan 25) = 100tan 25
=> b = 100 (tan 25 / tan29 - tan25) => b = 100 (0.466 / 0.554 - 0.466) = 527.6
m
Height h = 527.69 x tan 29 = 292.5 m
Tallness of Mesa = h + 1.8 = 294.3 m

Answer 2

Let our equation be: y = x tan 29

and the step by step solution is:

y = (x + 100) tan 25

x tan 29 = (x + 100) tan 25

x tan 29 = x tan 25 + 100 tan 25

x tan 29 - x tan 25 = 100 tan 25

x(tan 29 - tan 25) = 100 tan 25

x = 100 tan 25 / (tan 29 - tan 25) = 529.887 m

y = x tan 29 = 293.72 m

height of mesa is now computed as

= y + 1.8 = 295.52 or 296 m