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
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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) (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.
and .
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) (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
, which is really 3 equations in one.
-->-->-->-->
At this point, using the approximate values , you could calculate (rounded),
but you do not need to report/write the value for , so you can keep calculating (just multiply times ) to get as shown below.
--->
Using the approximate values ,
---> (rounded).
The height of the building is 327 meters.
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