SOLUTION: From a point on the ground, the angle of elevation of the top of a builing is 28 degrees. From another point 64 m nearer to the building, the angle of elevation of the top is 58 de

Algebra ->  Trigonometry-basics -> SOLUTION: From a point on the ground, the angle of elevation of the top of a builing is 28 degrees. From another point 64 m nearer to the building, the angle of elevation of the top is 58 de      Log On


   

Question 473458: From a point on the ground, the angle of elevation of the top of a builing is 28 degrees. From another point 64 m nearer to the building, the angle of elevation of the top is 58 degrees. Find the height of the building.
Please show your steps itll be helpful
Answer by lwsshak3(11628) About Me  (Show Source):
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From a point on the ground, the angle of elevation of the top of a builing is 28 degrees. From another point 64 m nearer to the building, the angle of elevation of the top is 58 degrees. Find the height of the building.
Please show your steps itll be helpful.
**
Draw a right triangle with the vertical leg representing the height y of the building.
Draw a horizontal leg divided into two parts.
The angle of elevation from the far end to the top of the bldg is 28º.
64 m closer the angle of elevation is 58º
distance from the building to the 58º point =x
distance from the building to the 28º point =x+64
You now have two right triangles to work with.
..
tan 28º=y/x+64
y=tan 28º*(x+64)
..
tan 58º=y/x
y=tan 58º*x
..
tan 28º*(x+64)=tan 58º*x
.5317x+34.0294=1.6003x
1.0686x=34.0294
x=34.0294/1.0686=31.8438
y=tan 58º*x=50.96 ft
ans:
Height of building=50.96 ft