A 35-foot tall pole is leading towards a building. To stop the pole from leaning
1 answer:
9514 1404 393
Answer:
38.5°
Step-by-step explanation:
You are given all three side lengths of the relevant triangle, so the Law of Cosines can be used to find any desired angle. If we call the desired angle C, then that law tells you ...
C = arccos((a² +b² -c²)/(2ab))
where a and b are the triangle side lengths adjacent to the angle of interest, and c is the side opposite. Here, 'a' and 'b' are the pole and cable lengths, and 'c' is the distance of the stake from the pole.
C = arccos((35² +48² -30²)/(2·35·48)) = arccos(2629/3360)
C ≈ 38.515°
The cable makes an angle of about 38.5° with the pole.
You might be interested in
Answer:
1. -2/3 3. -5/4 5. 3/2 FOR THE REST OF THE PARTS LOOK THROUGH THE EXPLANATIONS
Step-by-step explanation:
Before I start the workings, I'll give a little explanation on this topic.
So, the equation of a straight line is
y = mx + c
where x and y are any coordinates of any point on the line.
m is the gradient or slope
m can be calculated using 2 formulas,
formula 1: Rise/Run
where rise is the how much a graph goes upwards or downwards, if its upwards use positive integer and if its downwards use negative integer.
Run is how much a graph moves to the right or to the left, if it moves to the right is is positive, if it moves to the left it is negative.
Formula 2: (y2-y1)/(x2-x1)
the values of these are taken through any 2 coordinates on the line.
and c is the y-intercept(the point where the line crosses the y-axis.
<u>MOVING TO ANSWERING NOW</u>
1. Dotted points on the line are (1,0) and (4,-2)
Formula of slope,
U can use any of the 2 formulas given above
I'll show both for this question
m = (y2-y1)/(x2-x1) = (-2-0)/(4-1) = -2/3
OR
m = rise/run = where rise is -2 and run is 3 so -2/3
2. TRY DOING THIS ONE YOURSELF
For the next part I'll do 3 and 5 for your understanding, try doing 2 and 4 on your own to understand.
3. Coordinates given (13,1) and (1,16)
m = (y2-y1)/(x2-x1) = (16-1)/(1-13) = 15/-12 simplify this and it becomes -5/4
5. (-8,-14) and (-10,-17)
m = (y2-y1)/(x2-x1) = (-17-(-14))/(-10-(-8)) = -3/-2 = 3/2
FOR THE NEXT PART I'LL DO 7,8 AND 10 FOR YOU, TRY DOING 9 ON YOUR OWN FOR PRACTICE.
I WILL ALSO ATTACH FILES FOR THE NEXT PARTS IN ORDER OF QUESTIONS SO SEE THEM.
7. y = x + 3 this means y = 1x +3 which means:
1 is the gradient
3 is the y-intercept
so 1 as a fraction is 1/1 which means rise is one upwards and run is 1 to the right.
Now go to the graph on the y-axis and plot the point 3, (0,3) is your y-intercept. From their rise by one and run by one this will lead u to point (1,4)
Mark both these points and make a line through them.
8. x = -5
now look at this equation in the form of y = mx + c
0 = 1x + 5 the means y is 0 and it is already told in the question that x = -5
if u rearrange 0 = 1x + 5 it will give you x = -5
now when y is 0 x = -5 put a point on the coordinate (-5,0) and draw a vertical straight line.
10. y = (1/4)x - 1
slope is 1/4 which means rise is 1 and run is 4
y-intercept is -1
now go to y=-1 which is the coordinate (0,-1) and rise by one and run by 4, this will take u to the coordinate (4,0) now put a dot on both coordinates, connect them and put a line through them.
