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.

Result

x =  159 km

Solution:

$u = (84 \cdot \cos 17; 84 \cdot \sin 17) = (80.33; 24.559) \ \\ v = (135 \cdot \cos 107; 135 \cdot \sin 107) = (-39.47; 129.101) \ \\ x=|u+v| = \sqrt{ (80.33+(-39.47))^2+ (24.559+129.101)^2 } = 159 \ \text{km} \ \\$

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!

Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Be the first to comment!

Tips to related online calculators
Two vectors given by its magnitudes and by included angle can be added by our vector sum calculator.
Pythagorean theorem is the base for the right triangle calculator.

Next similar math problems:

An airplane leaves an airport and flies to west 120 miles and then 150 miles in the direction S 44.1°W. How far is the plane from the airport (round to the nearest mile)?
2. Theorem prove
We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?
Given that P = (5, 8) and Q = (6, 9), find the component form and magnitude of vector PQ.
4. Vector 7
Given vector OA(12,16) and vector OB(4,1). Find vector AB and vector |A|.
5. Reference angle
Find the reference angle of each angle:
6. Angle between vectors
Find the angle between the given vectors to the nearest tenth of a degree. u = (-22, 11) and v = (16, 20)
7. The pond
We can see the pond at an angle 65°37'. Its end points are 155 m and 177 m away from the observer. What is the width of the pond?
8. Steeple
Steeple seen from the road at an angle of 75°. When we zoom out to 25 meters, it is seen at an angle of 20°. What is high?
9. Angles by cosine law
Calculate the size of the angles of the triangle ABC, if it is given by: a = 3 cm; b = 5 cm; c = 7 cm (use the sine and cosine theorem).
10. Scalar dot product
Calculate u.v if |u| = 5, |v| = 2 and when angle between the vectors u, v is: a) 60° b) 45° c) 120°
11. Cotangent
If the angle α is acute, and cotg α = 1/3. Determine the value of sin α, cos α, tg α.
12. Vector sum
The magnitude of the vector u is 12 and the magnitude of the vector v is 8. Angle between vectors is 61°. What is the magnitude of the vector u + v?
13. Scalene triangle
Solve the triangle: A = 50°, b = 13, c = 6
14. Angles
In the triangle ABC, the ratio of angles is: a:b = 4: 5. The angle c is 36°. How big are the angles a, b?
15. Greatest angle
Calculate the greatest triangle angle with sides 197, 208, 299.
16. Trigonometry
Is true equality? ?
17. Side c
In △ABC a=2, b=4 and ∠C=100°. Calculate length of the side c.