brenda walks 7km for a bearing of 120degrees then 9km for a bearing of 180degrees.Calculate distance and and bearing?
bearing 40degree
distance 46km
the bearing has to be between 120º and 180º
she walked 16 km total , so the distance must be less than that
40º and 46 km makes no sense
use N/S and E/W components of each segment of the trip to find the total resultant
D = 7km[120o] + 9km[180o].
X = 7*sin120 + 9*sin180 = 6.06 km.
Y = 7*Cos120 * 9*Cos180 = -12.5 km.
D = 6.06 - 12.5i = 13.9km[-25.9o] = 13.9km[25.9o] S. of E. = 13.9km[103.5o] CW(bearing).
Tan A = X/Y.
To calculate the total distance Brenda walks and her final bearing, we can break down her journey into two separate legs and use trigonometry.
For the first leg, we have the distance (7 km) and the bearing (120 degrees). We can use the cosine rule to find the horizontal (x) and vertical (y) components of this leg:
x = 7 * cos(120 degrees) = -3.5 km (negative because it's to the left)
y = 7 * sin(120 degrees) = 6.06 km
For the second leg, we have the distance (9 km) and the bearing (180 degrees). Similarly, we can find the horizontal and vertical components:
x = 9 * cos(180 degrees) = -9 km
y = 9 * sin(180 degrees) = 0 km
To calculate the total distance, we add the horizontal and vertical components of each leg:
Total distance (d) = sqrt((-3.5 - 9)^2 + (6.06 + 0)^2)
= sqrt(12.25 + 36.7236)
= sqrt(48.9736)
≈ 7 km
To calculate the final bearing, we can use the atan2 function to find the angle between the final position and the starting position:
Final bearing = atan2((6.06 + 0), (-3.5 - 9)) = atan2(6.06, -12.5)
≈ -26.36 degrees (rounded to two decimal places)
Therefore, Brenda walks a total distance of approximately 7 km and her final bearing is about -26.36 degrees.