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
Anettt [7]
3 years ago
11

Two airplanes leave an airport at the same time, the first headed due north and the second at a bearing of N42^ E . At 2:00PM, t

he first airplane is 312 miles from the airport while the second airplane is 487 miles from the airport. Assuming both followed linear paths from the airport, how far apart are the two airplanes at 2:00PM?
Mathematics
1 answer:
Leno4ka [110]3 years ago
3 0

Answer:

The two airplanes are about 330miles apart.

Step-by-step explanation:

The diagram interpreting the question has been attached to this response.

As shown in the diagram,

i. the airplanes leave at point C.

ii. at 2.00pm the first and second airplanes are at points A and B respectively, where they are 312miles and 487miles away from the starting point C in directions due north and N42E from the point C.

iii. the points A, B and C form a triangle with sides a, b and c.

To solve for the value of c which is the distance between the two planes at 2.00pm, the cosine rule is used.

c² = a² + b² - 2abcosC            --------------(i)

where;

b  = 312miles

a = 487miles

C = 42°

Substitute these values into equation (i) and solve as follows;

c² = (487)² + (312)² - 2(312)(487)cos(42)

c² = (237169) + (97344) - 303888cos(42)

c² = (237169) + (97344) - 303888(0.7431)

c² = 334513 - 225819.1728

c² = 108693.8272

<em>Take the square root of both sides</em>

√c² = √108693.8272

c = 329.69

c ≅ 330miles

Therefore, the two airplanes are far apart by 330miles

You might be interested in
3/5 × -4/7 + 4/35 - 3/10 × 4/7
Annette [7]

Answer:

I think its -2/5 but not sure

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Based on Charles Waddell Chestnutt's "The Wife Of His Yout. Which of the following statements about Mr. Ryder is true? Choose al
Serjik [45]
I'm pretty sure that there are two statements which are true: b. At the conclusion of the story, Charles Waddell Chesnutt wants readers to see the redeeming qualities in Mr. Ryder. and c. The wife of Mr. Ryder's youth could never be a member of his exclusive society.
3 0
3 years ago
5.7y-5.2=y/2.5 how to solve
11Alexandr11 [23.1K]

5.7y-5.2=y/2.5

Add 5.2 to both sides:

5.7y = y/2.5 + 5.2

y/2.5 = 0.4y

5.7y = 0.4y + 5.2

Subtract 0.4y from both sides:

5.3y = 5.2

Divide both sides by 5.3:

y = 5.2/5.3

y = 0.98113

3 0
2 years ago
Read 2 more answers
If 4 gallons of milk cost $16.76 how much would 7 gallons of milk cost
professor190 [17]
$16.76 divided by 4 = $4.19 each gallon
So $4.19 x 7 gallons = $29.33
8 0
3 years ago
A 32 foot tall tree casts a shadow that is 48 feet long. How far away from the tree is a
sveticcg [70]

Answer:

39 feet

Step-by-step explanation:

take the tree as AB , the distance between the man and the tree as BC, the distance between the man and the tip of the shadow CD and the point intersecting the hypotenuse CE

since CE parallel to AB we can BPT

CE/AB = CD/BD

6/32= CD/48

CD = 9 feet

since CD is feet

BC is 48-9 = 39 feet

3 0
2 years ago
Other questions:
  • Tamika has a hard rubber ball whose circumference measures 13 inches. she wants to box it for a gift but can only find cube-shap
    14·1 answer
  • Carson made a four digit number with a 4 in th thousands place, a 4 in the on the ones place,a 5 in the tens place, and a 6 in t
    14·2 answers
  • How many community serviece hours are students required to work ? ex
    14·1 answer
  • 5. If mFBA= 7x + 6y. what is mFBA<br> 40<br> 44<br> 47<br> 60
    7·2 answers
  • What is the length of HL ?
    8·2 answers
  • How many different ways can the first 12 letters of the alphabet be arranged?
    5·1 answer
  • How is this equation completed? I cannot find any examples in the book.
    10·1 answer
  • The mean is defined as the
    9·1 answer
  • Which of the following is an irrational number?<br> A. 3/14<br> B. square root of 38<br> C. 3.8
    5·1 answer
  • Im just looking for 25/4 (that's a fraction) divided in 3.
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!