A plane flies 90km on a bearing 030 degree and then flies 150km due east. How far east of the starting point is the plane?
^&%#*& mathematicians !
He flies on a HEADING of 030 east of north, NOT a bearing. You take a bearing on something, its direction from you. You sail or fly a compass HEADING.
anyway
East components are
90 sin 30 +150
=90 * (1/2) + 150
= 45 + 150
= 195 km east of start
D = 90km[30o] + 150km[0o]
X = 90*Cos30 + 150 = 228 km.
Y = 90*sin30 = 45 km.
Tan A = Y/X = 45/228 = 0.19742
A = 11.17o
D=X/CosA = 228/Cos11.17=232 km[11.17o]
Dx = 232*cos11.17 = 227.998 km East of
starting point.
Henry,
The 30 degrees is from North (the y axis), not from east (the x axis as in math convention).
Thanks! I thought it was 30o from the
x axis, because the problem didn't say
30o East of North.
Use a graph of f or some other method to determine what, if any, value to assign to f(a) to make f continuous at x = a. HINT [See Example 2.] (If there is no such value, enter NONE.)
f(x) =
x2 − 18x + 81
x − 9
; a = 9
I want the answer now
With diagrams
I don't understand why u got the answer
To determine how far east of the starting point the plane is, we can break down the problem into two separate movements: the initial leg flying on a bearing of 030 degrees, and then the second leg flying due east.
1. Initial leg flying on a bearing of 030 degrees:
A bearing of 030 degrees means that the plane is flying at an angle of 30 degrees north of due east.
To determine the horizontal distance traveled, we can use trigonometry. In a right-angled triangle, the cosine of an angle gives the ratio of the adjacent side to the hypotenuse.
Let's use the cosine function: cos(30) = adjacent/hypotenuse.
We know the hypotenuse is the distance traveled on this leg, which is 90 km.
So, cos(30) = adjacent/90.
To solve for the adjacent side, multiply both sides of the equation by 90:
90 * cos(30) = adjacent.
Adjacent = 90 * cos(30) ≈ 77.94 km.
2. Second leg flying due east:
The plane is flying due east for a distance of 150 km. Since it's flying directly east, the entire distance is eastward.
To determine the total distance east of the starting point, we add the distances traveled in each leg:
77.94 km + 150 km = 227.94 km.
Therefore, the plane is approximately 227.94 km east of the starting point.