1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Lapatulllka [165]
2 years ago
10

A ship leaves port at noon and has a bearing of S29oW. The ship sails at 20 knots. How many nautical miles south and how many na

utical miles west will the ship have traveled by 6:00 PM
Mathematics
1 answer:
ira [324]2 years ago
7 0

Answer:

Approximately 58.2\; \text{nautical miles} (assuming that the bearing is {\rm S$29^{\circ}$W}.)

Step-by-step explanation:

Let v denote the speed of the ship, and let t denote the duration of the trip. The magnitude of the displacement of this ship would be v\, t.

Refer to the diagram attached. The direction {\rm S$29^{\circ}$W} means 29^{\circ} west of south. Thus, start with the south direction and turn towards west (clockwise) by 29^{\circ} to find the direction of the displacement of the ship.

The hypothenuse of the right triangle in this diagram represents the displacement of the ship, with a length of v\, t. The dashed horizontal line segment represents the distance that the ship has travelled to the west (which this question is asking for.) The angle opposite to that line segment is exactly 29^{\circ}.

Since the hypotenuse is of length v\, t, the dashed line segment opposite to the \theta = 29^{\circ} vertex would have a length of:

\begin{aligned}& \text{opposite (to $\theta$)} \\ =\; & \text{hypotenuse} \times \frac{\text{opposite (to $\theta$)}}{\text{hypotenuse}} \\ =\; & \text{hypotenuse} \times \sin (\theta) \\ =\; & v\, t \, \sin(\theta) \\ =\; & v\, t\, \sin(29^{\circ})\end{aligned}.

Substitute in \begin{aligned} v &= 20\; \frac{\text{nautical mile}}{\text{hour}}\end{aligned} and t = 6\; \text{hour}:

\begin{aligned} & v\, t\, \sin(29^{\circ}) \\ =\; & 20\; \frac{\text{nautical mile}}{\text{hour}} \times 6\; \text{hour} \times \sin(29^{\circ}) \\ \approx\; & 58.2\; \text{nautical mile}\end{aligned}.

You might be interested in
4p + 1 > −7 or 6p + 3 < 33?
aleksandr82 [10.1K]
P>-2 or p < 5 is your answer 
4 0
3 years ago
Two true or false :)
asambeis [7]
1. false because they have the same slope and y-intercept so they have infinite number of solutions
2. true
4 0
3 years ago
Is this correct ? if not what’s the correct answer?
lara [203]
Yes this is correct because that angle in is with the other angles to
5 0
2 years ago
Read 2 more answers
Please HELP MEEEE!!
vladimir1956 [14]

Answer:

oh go on quizlet and look

Step-by-step explanation i saw it there

7 0
2 years ago
Would my answer be c or a
mylen [45]

the answer is c

the y-intercept is 10–it doesn’t have a negative sign, so it is positive

4 0
3 years ago
Other questions:
  • Carmen is at a used bookstore. Paperback books cost $ 1 each, and hardcover books cost $ 2 each. Carmen can spend up to $ 10 in
    6·2 answers
  • What is the surface area of the cylinder in terms of pi? The diagram is not drawn to scale.
    9·1 answer
  • a contract is good in the base of a circular fountain on the blueprint the base of the food has a date diameter of 18 cm the boo
    5·1 answer
  • Gcf of 30x2,6x6,18x2
    14·1 answer
  • The function f(x) = x2 is graphed above. Which of the graphs below represents the function g(x) = (x + 1)2
    10·1 answer
  • PLEASE HELP ASAP!<br> Classify the polynomial, 8m^3–10m^2– 7, by degree and number of terms.
    5·1 answer
  • Add<br>3×+8y-12zand5x-7y+15z<br>help meee<br>​
    12·1 answer
  • FIND THE SLOPE of the line that passes through the points (1,-19) and (-2,-7). You do not need to write the whole equation
    10·2 answers
  • Please help!! quizz thanks if you do
    7·1 answer
  • A box contains 18 green marbles and 8 white marbles. If the first marble chosen was a white marble, what is the probability of c
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!