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
OlgaM077 [116]
3 years ago
13

A train leaves train station A and heads due west for 105 miles to reach train station B. Another train leaves train station A a

t the same time and travels 85 miles to train station C in a direction 45° north of west from station A. To the nearest mile, how far is train station C from train station B?
75 miles
109 miles
135 miles
176 miles

Mathematics
2 answers:
ioda3 years ago
4 0

Answer:

Option (a) is correct.

To the nearest mile, the distance between train station C from train station B is 75 miles.

Step-by-step explanation:

 Given : A train leaves train station A and heads due west for 105 miles to reach train station B. Another train leaves train station A at the same time and travels 85 miles to train station C in a direction 45° north of west from station A.

We have to find the distance between train station C from train station B.

We first draw the position of stations according to given statement.

Figure shown below in attachment.

Since we have to find the distance BC , Let BC = x

For a triangle ABC, with ∠A = 45° and AB = 105 m and AC = 85 m

Using Cosine rule,

BC=\sqrt{CA^2+AB^2-2\cdot AB\cdot AC\cdot \cos A }

Substitute, we have,

x=\sqrt{(85)^2+(105)^2-2\cdot 85\cdot 105\cdot \cos 45^{\circ}}

Simplify , we have,

x=75.020

Thus, to the nearest mile, the distance between train station C from train station B is 75 miles.

Vilka [71]3 years ago
3 0
Hello,

Answer A

Theorem of Al Kashi gives:

x²=105²+85²-2*105*85*√2/2=5628.14395...
x=75.0209... (mi)
You might be interested in
What is the solution to the equation -2n -2 / 3 =12 ? n =
SVEN [57.7K]
The answer is n= -19/3
3 0
3 years ago
One month Lisa rented 2 movies and 3 video games for a total of $26. The next month she rented 6 movies and 5 video games for a
xxMikexx [17]

Answer:rental cost for movie $5.50 rental cost for video game $5.00

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Each bag of apples weighs 4 1/2 lb how much do 6 bags weigh?
Serjik [45]

Answer:

The bags would weigh 27lbs. multiply 4 1/2 and6 and you get 27lbs.

4 0
3 years ago
Read 2 more answers
Margie needs 7 ticket to the same soccer game.
Ivahew [28]
Do 3 divided by 53 to find the cost of one ticket and then multiply the that number with 7
7 0
2 years ago
Read 2 more answers
What does “4(x+3)+5x-x^2 “equal
Nikitich [7]

Answer:

Thanks for asking!

Step-by-step explanation:

The answer is -x²+9+12

5 0
2 years ago
Other questions:
  • An independent-measures study with n = 8 in each treatment produces M = 75 for the first treatment and M = 71 for the second tre
    12·1 answer
  • Create the equation used to graph this graph:
    13·1 answer
  • Distance between 0,2 and 8,8
    6·1 answer
  • It's the one that says 25 plz help me it's under number 24
    9·1 answer
  • Solve 0=2y−8x+10 for y
    7·1 answer
  • If x= 2 what does y equal
    14·1 answer
  • 2) A farmhouse shelters 61 animals. Some are cows and some are ducks. Altogether there are
    6·1 answer
  • Evaluate the expression if g-=2, r=3, and t=. 3ab+c^2/a
    11·1 answer
  • Solve the following equation -3x+5<20
    13·1 answer
  • Tickets for a community theater cost $14 for each main floor seat and $6 for each balcony seat. There are 500 seats on the main
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!