I'm hoping someone can tell me what they mean "edge of the building" in the following word problem:
A man late for a meeting is running to the office. The angle of elevation to the
top of the building is 54 degrees and the angle of depression to the foot of the
building is 18 degrees. The building is 45 ft tall. Determine how far the man is
from the edge of the building to the nearest tenth of a foot.Here is a replicate of the drawing that is given:
I did the following to get all of the angles:
$$180^\circ - 90^\circ - 54^\circ = 36^\circ$$ $$180^\circ - 90^\circ - 18^\circ = 72^\circ$$
Then I did $54^\circ + 18^\circ$ to get $72^\circ$ and I was able to get the acute following triangle:
Now my question is not how far the man is from the edge of the building, but what part(s) of the triangle do I need to know to get how far the man is from the edge of the building? Any ideas?
$\endgroup$ 42 Answers
$\begingroup$The edge of the building is the horizontal distance. Like if I said "I'm 30 feet from the edge of the river," it's understood that this means 30 feet perpendicular to the river edge.
$\endgroup$ 2 $\begingroup$If $x$ is the unknown horizontal distance, the 45ft vertical height of building is the sum of two lengths, of the segments above and below the horizontal line of length $x$. The ratio of each of those segment lengths to $x$ is some basic trigonometric function of the angles in the two small triangles, and the angles are known, so you can determine the ratio between $x$ and the height of the building.
The high-level idea is that the whole figure can be scaled up or down, keeping the ratios of all pairs of segments the same, so that one length (the height of the building) should be enough to determine everything, given the angles and enough patience to work out the relative size of enough parts of the diagram.
$\endgroup$
