Two lighthouses are located 20 miles from one another on a north-south line. If a boat is spotted S 25o E from the northern ligh
1 answer:
Answer:
The southern lighthouse is 3.4 miles closer than the northern lighthouse
Step-by-step explanation:
From the figure we see that we need to find the distances AK and BK.
The measure of the third angle K is = 180- 25-35= 120 degrees
Using the sine ratios we can find the two distances
From the figure
The northern distance is given by
20/ sin 120 = kA/ sine 35
KA= 20 sine 35/ sine 120
KA= 13.25 miles
The southern distance is given by
20 /sine 120= KB / sine 25
20 sine 25/ sine 120 = KB
KB= 9.759=9.76 miles
Difference between the two miles =
13.25 miles - 9.76 miles = 3.49 miles
The southern lighthouse is 3.4 miles closer than the northern lighthouse
Option C is correct
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Answer:
(y+7)=5/6(x+6)
Step-by-step explanation:
For this problem we need to use Point-Slope Form to write an equation.
We already have the point, (-6,-7), so all we need now is the slope, which we know is perpendicular to the line 6x+5y=30.
First, let's find the slope of 6x+5y=30 by converting it into Slope-Intercept Form, which is y=mx+b. m is the slope.
6x+5y=30
5y=-6x+30
y=-6/5x+6
So the slope of this line is -6/5, but we need the slope of the line is perpendicular to this line.
When a line is perpendicular to another, their slopes are negative reciprocals to one another, or opposite reciprocals. For example, a line that is perpendicular to another line that has a slope of 3/4 will have a slope of -4/3. Flip the numerator and denominator to find the reciprocal and add a negative.
x
So the negative reciprocal of -6/5 is 5/6, so that is our slope.
Now we can assemble our equation, here is the Point-Slope Form:
again, m is our slope.
and
represent the coordinates of the point that this line passes through, (-6, -7).
Let's plug in the y, x, and m values:
(y-(-7))=5/6(x-(-6))
Simplify:
(y+7)=5/6(x+6)
That is our final answer.