Bearing

A plane flew 50 km on a bearing 63°20' and the flew on a bearing 153°20' for 140km. Find the distance between the starting point and the ending point.

Correct result:

s =  148.661 km

Solution:

A=63+20/60=1903≐63.3333 ∘ B=153+20/60=4603≐153.3333 ∘ x1=50⋅ cos⁡A∘=50⋅ cos⁡63.3333333333∘ =50⋅ 0.448799=22.43996 y1=50⋅ sin⁡A∘=50⋅ sin⁡63.3333333333∘ =50⋅ 0.893633=44.68163 x2=140⋅ cos⁡B∘=140⋅ cos⁡153.333333333∘ =140⋅ (−0.893633)=−125.10857=(−229422π/5761) y2=140⋅ sin⁡B∘=140⋅ sin⁡153.333333333∘ =140⋅ 0.448799=62.83189 x=x1+x2=22.44+(−125.1086)≐−102.6686 km y=y1+y2=44.6816+62.8319≐107.5135 km s=x2+y2=(−102.6686)2+107.51352=10 221=148.661 kmA=63+20/60=\dfrac{ 190 }{ 3 } \doteq 63.3333 \ ^\circ \ \\ B=153+20/60=\dfrac{ 460 }{ 3 } \doteq 153.3333 \ ^\circ \ \\ x_{1}=50 \cdot \ \cos A ^\circ =50 \cdot \ \cos 63.3333333333^\circ \ =50 \cdot \ 0.448799=22.43996 \ \\ y_{1}=50 \cdot \ \sin A ^\circ =50 \cdot \ \sin 63.3333333333^\circ \ =50 \cdot \ 0.893633=44.68163 \ \\ x_{2}=140 \cdot \ \cos B ^\circ =140 \cdot \ \cos 153.333333333^\circ \ =140 \cdot \ (-0.893633)=-125.10857=(-229422π/5761) \ \\ y_{2}=140 \cdot \ \sin B ^\circ =140 \cdot \ \sin 153.333333333^\circ \ =140 \cdot \ 0.448799=62.83189 \ \\ x=x_{1}+x_{2}=22.44+(-125.1086) \doteq -102.6686 \ \text{km} \ \\ y=y_{1}+y_{2}=44.6816+62.8319 \doteq 107.5135 \ \text{km} \ \\ s=\sqrt{ x^2+y^2 }=\sqrt{ (-102.6686)^2+107.5135^2 }=10 \ \sqrt{ 221 }=148.661 \ \text{km}

Try another example


Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!





Please write to us with your comment on the math problem or ask something. Thank you for helping each other - students, teachers, parents, and problem authors.

Showing 0 comments:
avatar




Tips to related online calculators
For Basic calculations in analytic geometry is helpful line slope calculator. From coordinates of two points in the plane it calculate slope, normal and parametric line equation(s), slope, directional angle, direction vector, the length of segment, intersections the coordinate axes etc.
Two vectors given by its magnitudes and by included angle can be added by our vector sum calculator.
Try our complex numbers calculator.
Pythagorean theorem is the base for the right triangle calculator.
See also our trigonometric triangle calculator.

You need to know the following knowledge to solve this word math problem:


 
We encourage you to watch this tutorial video on this math problem: video1   video2

Next similar math problems:

  • Bearing - navigation
    navigation A ship travels 84 km on a bearing of 17°, and then travels on a bearing of 107° for 135 km. Find the distance of the end of the trip from the starting point, to the nearest kilometer.
  • Medians and sides
    taznice3 Triangle ABC in the plane Oxy; are the coordinates of the points: A = 2.7 B = -4.3 C-6-1 Try calculate lengths of all medians and all sides.
  • Add vector
    vectors_2 Given that P = (5, 8) and Q = (6, 9), find the component form and magnitude of vector PQ.
  • Imaginary numbers
    Complex_conjugate_picture.svg Find two imaginary numbers whose sum is a real number. How are the two imaginary numbers related? What is its sum?
  • Vector 7
    vectors_sum0_1 Given vector OA(12,16) and vector OB(4,1). Find vector AB and vector |A|.
  • Triangle ABC
    lalala In a triangle ABC with the side BC of length 2 cm The middle point of AB. Points L and M split AC side into three equal lines. KLM is isosceles triangle with a right angle at the point K. Determine the lengths of the sides AB, AC triangle ABC.
  • De Moivre's formula
    sqrt3_complex There are two distinct complex numbers z such that z3 is equal to 1 and z is not equal 1. Calculate the sum of these two numbers.
  • ABS CN
    complex_num Calculate the absolute value of complex number -15-29i.
  • Complex number coordinates
    complex_numbers Which coordinates show the location of -2+3i
  • The right triangle
    rt_triangle_1 In the right triangle ABC with right angle at C we know the side lengths AC = 9 cm and BC = 7 cm. Calculate the length of the remaining side of the triangle and the size of all angles.
  • Unit vector 2D
    one_1 Determine coordinates of unit vector to vector AB if A[-6; 8], B[-18; 10].
  • Triangle IRT
    triangles_5 In isosceles right triangle ABC with right angle at vertex C is coordinates: A (-1, 2); C (-5, -2) Calculate the length of segment AB.
  • Euclid2
    euclid In right triangle ABC with right angle at C is given side a=27 and height v=12. Calculate the perimeter of the triangle.
  • RT triangle and height
    345 Calculate the remaining sides of the right triangle if we know side b = 4 cm long and height to side c h = 2.4 cm.
  • Vectors
    green For vector w is true: w = 2u-5v. Determine coordinates of vector w if u=(3, -1), v=(12, -10)
  • Triangle and its heights
    triangle_2 Calculate the length of the sides of the triangle ABC, if va=5 cm, vb=7 cm and side b is 5 cm shorter than side a.
  • Vector
    vectors Determine coordinates of the vector u=CD if C[19;-7], D[-16,-5].