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
ollegr [7]
3 years ago
15

Island A is 250 miles from island B. A ship captain travels 260 miles from island A and then finds that he is off course and 160

miles from island B. What bearing should he turn to, so he is heading straight towards island B?
A. 111.65
B. 119.84
C. 21.65
D. 135.53

Mathematics
2 answers:
AnnyKZ [126]3 years ago
8 0

Answer:

A. 111.65

Step-by-step explanation:

This scenario can be interpreted like a triangle ABC where A and B are islands and C is the point from where the captain is 160 miles from island B.

a = 160

b = 260

c = 250

Law of cosines

c^2 = a^2 + b^2 - 2(ab)Cos(C)\\Arranging\ as\\2ab \ cos\ C = a^2+b^2-c^2\\2(160)(260)\ cos\ C = (160)^2+(260)^2- (250)^2\\83200\ cos\ C=25600+67600-62500\\83200\ cos\ C=30700\\cos\ C= \frac{30700}{83200}\\cos\ C=0.36899\\C = arccos\ (0.36899)\\C = 68.35

The internal angle is 68.35°

We have to find the external angle to find the bearing the captain should turn

Using the rule of supplimentary angles:

The external angle = 180 - 68.35 = 111.65°

Therefore, the captain should turn 111.65° so that he would be heading straight towards island B.

Hence, option 1 is correct ..

PIT_PIT [208]3 years ago
3 0

Answer: Option 'a' is correct.

Step-by-step explanation:

Since we have given that

AB = 250 feet

AC = 260 feet

BC = 160 feet

We need to find the angle C that is heading straight towards island B.

We will apply "Law of cosine":

\cos C=\dfrac{a^2+b^2-c^2}{2ab}\\\\\cos C=\dfrac{160^2+260^2-250^2}{2\times 160\times 260}\\\\\cos C=0.368\\\\C=\cos^{-1}(0.368)\\\\C=68.40^\circ

Exterior angle would be

180-68.40=111.65^\circ

Hence, Option 'a' is correct.

You might be interested in
Can you help me please?
Kamila [148]

Answer: The set of all possible input values

Step-by-step explanation:

7 0
3 years ago
Indicate the method you would use to prove the two 's . If no method applies, enter "none".
Andrei [34K]
Answer: ASA method must be applied to the given triangles to prove then congruent.


In two triangles, if two angles and their included side are congruent then the two triangles are said to be congruent .This method is known as Angle-Side -Angle postulate(ASA).
In the given triangles one side with their corresponding angles are equal. Therefore by ASA postulate they are congruent.
There we can see no other sides are given equal therefore all the other options cannot be applied.

you are lucky I had this test yesterday and I have the answer is ASA my math teacher said it was fine
6 0
3 years ago
Round each decimal to the nearest whole number
4vir4ik [10]

Answer:

1. 1

2. 8

3. 13

Step-by-step explanation:

hope that helps

6 0
2 years ago
What is the value of (-12-6).-3.5?
Nastasia [14]

Answer:

-21.5

Step-by-step explanation:

-12-6=-18 minus 3.5=-21.5

8 0
3 years ago
Margot is sewing a ribbon on a seam along the perimeter of a square pillow. The side length of the pillow is 2x2 + 1 inches, and
Rasek [7]
19.25 inches I think i.t is

8 0
3 years ago
Read 2 more answers
Other questions:
  • Paula weighed 65.5 kilograms before she started training she as lost 3500grams how much does she weigh
    5·2 answers
  • An answer to a word problem
    11·1 answer
  • In the xy -plane above, point C has coordinates (6, 9). Which of the following is an equation of the line that contains points O
    7·1 answer
  • Trail mix is sold in 1 pound bags Mary will buy some trail mix And repackage it so that each of the 15 members of her hiking clu
    14·1 answer
  • How do u simplify √2/√3x
    10·1 answer
  • Which figure shows a reflection of pre-image DEFG over the x-axis?
    11·1 answer
  • What’s the measure of
    13·2 answers
  • The table shows a proportional relationship.
    10·1 answer
  • I’m really having trouble on this, can anyone help?
    12·1 answer
  • 10 points
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!