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Answer:
The length of LK is 52 units.
Step-by-step explanation:
According to the Euclidean Geometry, if two triangles are similar, then every pair of respective sides are proportional and reports the same ratio. In this case, we construct the following formula:
(1)
If we know that ,
and
, then the length of
is:
The length of LK is 52 units.
Answer:
See below
Step-by-step explanation:
Here I attach you the detailed solution.
For this we will need to use the following trigonometric properties and formulas:
sin (x-y) = sin (x) cos (y) - cos (x) sin (y)
tan(x) = sin(x)/cos(x)
cot(x) = 1/tan(x) = [tan(x)] ^(-1) = cos (x)/sin(x)
This properties can be found in any mathematics book and is valid to apply them here, and are the only tools we use to solve the problem. Its worth to note that we have to assume that cos(x)sin(y) is different from 0 in order to use it as a denominator.
For this case we have that the equation of a line in the slope form intersection is given by:
Where:
m: It's the slope
b: It is the cut point with the y axis.
In the green graph we observe that, then its equation is
We have the slope of the red line substituting two points:
Thus, the red line has equation
Finally, the blue line is
Answer:
Green line, y = 5x + 2
Red line, y = 2x + 3
Blue line, y = 3x + 3