+4 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?
I have looked it up online but... I don't really understand how they go their equation to start off from this problem... Please help me...
Let the height of the Mesa =x
Let the distance to the base of the Mesa = y
x / y = tan(29),,,,,,,,,,,,,,,,,,,(1)
x / (y+100) = tan(25)........(2)
Now, can you solve the above 2 simultaneous equations? Try it.
+199 Solving these equations gives us: x=y*tan(29), and x=(y+100)(tan25).
Use a unit circle to find the appropriate values. y should be approximately 529.9. Then, solve for x by plugging the value of y back in.
+37146 tan 29 = o/x o= opposite the height of the mesa (less stephan's 1.8 ht)
tan 25 = o/(100+x) solve both of these equations for 'o' and set them equal to each other
(100+x) tan 25 = x tan 29 solve for x = 529.87 m from the mesa
so now we know
tan 29 = o/529.87 o = 293.71....
add Stephan's height 1.8 + 293.71 m = 295.51 m = height of mesa
BUT..... don't forget to add the 1.8m height of Stephan once you find your answer !!
