Trigonometry-

Question

A vertical mast stands on horizontal ground. A surveyor standing due south of the mast measures the angle of elevation of the top as 37°28'. he walks in a direction N 79° 40' W to a point 72 m from the base of the mast which is now on a bearing of N 17° 50' E. Question- calculate the height of the mast.

Answer 1

Assuming the term "bearing" was not intended (based on the use of "N 17º 50'E" notation which is a "direction" value)...

I get 55.62 m

 

We need top view geometry to see triangle formed from mast base to 1st stop to then to the 2nd stop point... use directions (as opposed to bearings) given to set up the proper internal angle opposite the side of mast-to-stop1 (that takes two computations - I get 82.53 deg total there.  Then use Law of Sines to compute length of mast-to-stop1 (that's 72.57 m), and separate triangle from side view looking upward at mast at angle of 37.467 deg and mast-to-stop1 distance to set up the trig:  

tangent (37.47deg) = ht/72.57  then  

ht = .766*72.57 = 55.62m

 

Check my math ;)