SOLUTION: In traveling across a flat ground, you notice a building directly in front of you. Its angle of elevation (to the peak) is 79.63 degrees. After you walk 24 meters closer to the bui

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: In traveling across a flat ground, you notice a building directly in front of you. Its angle of elevation (to the peak) is 79.63 degrees. After you walk 24 meters closer to the bui      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 894562: In traveling across a flat ground, you notice a building directly in front of you. Its angle of elevation (to the peak) is 79.63 degrees. After you walk 24 meters closer to the building, the angle of elevation is 83.74 degrees. Find the height of the building.
Found 2 solutions by josgarithmetic, KMST:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
You may draw a figure of two triangles sharing a side y, a vertical length of the building. from bottom of y, x to the right is the angle of elevation 83.74; and continuing 24 more to the right, that point is at the angle of elevation 79.63.

This figure as described (and labeled) will give you these two equations.

highlight_green%28y%2Fx=tan%2883.74%29%29 and highlight_green%28y%2F%28x%2B24%29=tan%2879.63%29%29.

Solve each of these for x, and then equate the two expressions; so that you have one equation in the single variable, y. Now you can just solve for y, the height of the building.

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Here's the figure:
It has two right triangles: and
You can re-write the equations as
y=%28x%2B24%29%2Atan%2879.63%5Eo%29=x%2Atan%2883.74%5Eo%29 , which is really 3 equations in one.

%28x%2B24%29%2Atan%2879.63%5Eo%29=x%2Atan%2883.74%5Eo%29-->x%2Atan%2879.63%5Eo%29%2B24%2Atan%2879.63%5Eo%29=x%2Atan%2883.74%5Eo%29-->24%2Atan%2879.63%5Eo%29=x%2Atan%2883.74%5Eo%29-x%2Atan%2879.63%5Eo%29-->24%2Atan%2879.63%5Eo%29=x%2A%28tan%2883.74%5Eo%29-tan%2879.63%5Eo%29%29-->24%2Atan%2879.63%5Eo%29%2F%28tan%2883.74%5Eo%29-tan%2879.63%5Eo%29%29=x

At this point, using the approximate values system%28tan%2879.63%5Eo%29=5.464685%2Ctan%2883.74%5Eo%29=9.116232%29 , you could calculate x=35.917(rounded),
but you do not need to report/write the value for x , so you can keep calculating (just multiply times tan%2883.74%5Eo%29=9.116232 ) to get y as shown below.

---> y=24%2Atan%2879.63%5Eo%29%2Atan%2883.74%5Eo%29%2F%28tan%2883.74%5Eo%29-tan%2879.63%5Eo%29%29
Using the approximate values system%28tan%2879.63%5Eo%29=5.464685%2Ctan%2883.74%5Eo%29=9.116232%29 ,
y=24%2A5.464685%2A9.116232%2F%289.116232-5.464685%29 ---> highlight%28y=327.4%29 (rounded).
The height of the building is 327 meters.