8. (06.04 MC)
1 answer:
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Two lines are perpendicular between each other if their slopes fulfills the following property
where m1 and m2 represents the slopes of line 1 an 2, respectively.
To find the slope of a line we can write it in the form slope-intercept form
Our original line is
Then its slope is
Now we have to find the slope of the second line. Using the first property,
Then the second line has to have a slope of 8.
The options given to us are:
Then we have to determine which of these options have a slope of 8. To do that we write them in the slope-intercept form:
Once we have the options in the right form, we note that the only one of them that has a slope of 8 is the last one.
Then the line perpendicular to the original one is
Answer:
(a) 5.36°
(b) β = 84.64° -θ
(c) d = 58.36·sin(84.64° -θ)/sin(θ)
(d) see the attached table
Step-by-step explanation:
(a) The lean angle can be found from the definition of the sine function:
sin(α) = Opposite/Hypotenuse = (5.45 m)/(58.36 m) ≈ 5.36°
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(b) The angle β does not depend on d; it only depends on the angle θ. Since the sum of angles of a triangle is 180°, we have ...
θ + (90°+α) + β = 180°
β = 180° -90° -5.36° -θ
β = 84.64° - θ
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(c) The law of sines tells you ...
d/sin(β) = 58.36/sin(θ)
Using the above expression for β and multiplying by sin(β), we get ...
d = 58.36·sin(84.64° -θ)/sin(θ)
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This can be simplified, if desired, to ...
d = 58.10·cot(θ) -5.45
