I really need help solving the following geomtry problem if anyone can help me. It goes like this: Jake is standing on the ground by a mesa in the desert. He is 1.8 meters tall and sights the top of the mesa at 29 degrees. Jake steps back 100 meters and sights the top at 25 degrees. How tall is the mesa? We have been using sine, cosine, and tangent but when I draw out my picture, I seem not to have enough information to use them (no complete side). Am I reading this problem wrong?

Question

I really need help solving the following geomtry problem if anyone can help me.  It goes like this:  Jake is standing on the ground by a mesa in the desert.  He is 1.8 meters tall and sights the top of the mesa at 29 degrees.  Jake steps back 100 meters and sights the top at 25 degrees.  How tall is the mesa?  We have been using sine, cosine, and tangent but when I draw out my picture, I seem not to have enough information to use them (no complete side). Am I reading this problem wrong?

amistre64 · Answer

attachment

amistre64 · Answer

tan(25) = h/(100+d)

tan(29) = h/d

amistre64 · Answer

d = h/tan(29)

tan(25) = h/(100 +(h/tan(29)))

amistre64 · Answer

tan(25) = h/(100tan(29)+h)/tan(29))

tan(25) = tan(29)h / 100tan(29) +h

amistre64 · Answer

tan(25) (100tan(29)+h) = tan(29)h

amistre64 · Answer

100tan(25)tan(29) + tan(25)h = tan(29)h

100tan(25)tan(29) = tan(29)h - tan(25)h

100tan(25)tan(29) = h(tan(29) - tan(25))

100tan(25)tan(29)
--------------- = h.....and add the 1.8
tan(29) - tan(25)

amistre64 · Answer

295.521  give or take :)

anonymous · Answer

You are awesome!   Many thanks amistre 64.  I get it.  substitution!  Many thanks!

amistre64 · Answer

youre welcome :)

anonymous · Answer

Hey amistre64.  I am new here and I just wanted to say thanks again.  You are a life saver and I totally got it - okay, it took me some thinking, but I did get it.  How so these medals work?  I'd give you gold star if I could.  Thank you, thank you for being there so quickly for me!