Someone help me please
1 answer:
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Answer:
Find another point on the perpendicular line.
Step-by-step explanation:
Given an original line "m", and a point off the line "Q", in order to construct a second line "p", meant to be perpendicular to "m" through the point "Q", fundamentally, the only truly necessary step to construct a perpendicular line through is to find another point on the yet-to-be-found perpendicular line.
Most often, this is accomplished by exploiting the fact that "p" is the set of all points that are equidistant from any pair of points that are symmetric about "p".
Since the symmetry must be about "p", and we don't even know where "p" is, one often finds two points on "m" that are equidistant from "Q".
This can be accomplished by adjusting a compass to a fixed radius (larger than the distance from "Q" to "m"), and making an arc that intersects "m" in two places. Those two places will be equidistant from "Q", and are simultaneously on line "m". Thus, these two points, "A" & "B" are symmetric about "p".
Since "A" & "B" are symmetric about "p", they are equidistant from "p", and are on "m". One could try to find the point of intersection between "p" and "m" through construction, but this is unnecessary. We need only find a second point (besides "Q") that is equidistant from "A" & "B", which will necessarily be a point on "p", to form the line perpendicular to "m".
To do this, fix the compass with any radius, and from "A" make a large arc generally in the direction of "B", and make the same radius arc from "B" in the direction of "A" such that the two arcs intersect at some point that isn't "Q". This point of intersection we can call point "T", and the line QT is line "p", the line perpendicular to the original line, necessarily containing "Q".
Answer:
Step-by-step explanation:
The first thing we are going to do is to fill in the other angles that we need to solve this problem. You could find ALL of them but all of them isn't necessary. So looking at the obtuse angle next to the 35 degree angle...we know that those are supplementary so 180 - 35 = the obtuse angle in the small triangle. 180 - 35 = 145. Within the smaller triangle we have now the 145 and the 10, and since, by the Triangle Angle-Sum Theorem all the angles have to add up to equal 180, then 180 - (10 + 145) = the 3rd angle, so the third angle is 180 - 155 = 25. Now let's get to the problem. If I were you, I'd draw that out like I did to keep track of these angles cuz I'm going to name them by their degree. In order to find d, we need to first find the distance between d and the right angle. We'll call that x. The reference angle is 35, the side opposite that angle is 12 and the side we are looking for, x, is adjacent to that angle. So we will use the tan ratio to find x:
Isolating x:
so
x = 17.1377 m
Now we have everything we need to find d. We will use 25 degrees as our reference angle, and the side opposite it is 12 and the side adjacent to it is
d + 17.1377, so that is the tan ratio as well:
and simplifying a bit:
and a bit more:
d + 17.1377 = 25.73408 so
d = 8.59, rounded