A surveying crew is tasked to measure the height of a mountain. From a point on level ground, they measure the angle of elevation to the top of the mountain as 21(degrees)40(minutes). They move 500m closer and found that the angle of elevation is now 35(degrees)10(minutes). How high is the mountain?

I don't really need an answer, I just want to ask if this question involves both oblique triangles and right triangles to solve. Anyone care to verify this?

Question

A surveying crew is tasked to measure the height of a mountain. From a point on level ground, they measure the angle of elevation to the top of the mountain as 21(degrees)40(minutes). They move 500m closer and found that the angle of elevation is now 35(degrees)10(minutes). How high is the mountain?

I don't really need an answer, I just want to ask if this question involves both oblique triangles and right triangles to solve. Anyone care to verify this?

anonymous · Answer

tan(21d40m)=h/(500+x), tan35=h/x, 
 h=h
(500+x)tan(21d40m)=xtan35
500tan(21d40m)=xtan35-xtan(21d40m)
500tan(21d40m)=x[tan35-tan(21d40m)]
500tan(21d40m)/[tan35-tan(21d40m)]=x
x=655.71 meters

anonymous · Answer

Entropy, let me know if you have question

anonymous · Answer

That's clever bud, you equated the both h since the trig ratios for them would produce the same height right?

anonymous · Answer

yeah, i think you can also use cosine law or tangent law

anonymous · Answer

I thought it should be sine law

anonymous · Answer

thanks and good luck now Entropy

anonymous · Answer

You got two angles and a side (500m).

anonymous · Answer

yes its sine law im sorry..lol

anonymous · Answer

No problem sir, thanks anyway.