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
son4ous [18]
2 years ago
6

A boat travels N 31° E for 65 miles and then N 59° W for 102 miles. Find the distance of the boat from its starting point.

Mathematics
2 answers:
densk [106]2 years ago
7 0

note 1: N 31 E means you start facing directly north, then turn 31 degrees toward the east.

note 2: N 59 W means you start facing directly north, then turn 59 degrees toward the west.

Check out the attached image to see the diagram. We start at point A, we then move to point B (see note 1 above) traveling 65 miles. Then we move to point C (see note 2) traveling 102 miles. The goal is to find the distance from A to C which is side b. Side b is opposite angle B.

I have added points D, E and F to help label the angles in a meaningful way. Angle DAB is the angle "N 31 E" mentioned earlier. Angle ABF is congruent to angle DAB (AD || EF; alternate interior angle theorem), so it is also 31 degrees. Angle EBC is the angle "N 59 W" mentioned earlier.

-----------------------------------

We need to figure out angle ABC to be able to find the missing side.

Note that all the angles formed at point B can be combined to form a straight angle that is 180 degrees

(angle ABC) + (angle EBC) + (angle ABF) = 180

(angle ABC) + (59) + (31) = 180

(angle ABC) + 90 = 180

(angle ABC) + 90-90 = 180-90

angle ABC = 90

-----------------------------------

We now know that angle ABC is 90 degrees

Focusing on triangle ABC, the notation "angle ABC" is the same as "angle B".

So we can use this to find side AC (aka side b). Use the law of cosines to solve for b.

b^2 = a^2 + c^2 - 2*a*c*cos(B)

b^2 = 102^2 + 65^2 - 2*102*65*cos(90)

b^2 = 102^2 + 65^2 - 2*102*65*0

b^2 = 102^2 + 65^2 - 0

b^2 = 102^2 + 65^2

b^2 = 10404 + 4225

b^2 = 14629

b = sqrt(14629)

b = 120.950403058444

b = 121 <----------- rounding to the nearest whole number

-----------------------------------

The final answer is C) 121 miles which is approximate

ra1l [238]2 years ago
4 0

The directions of travel are at right angles to each other, so the Pythagorean theorem can be used to find the straight-line distance to the starting point. That distance (d) satisfies ...

d² = 65² +102²

d = √(4225 +10404) = √14629 ≈ 120.95

The appropriate choice is ...

... c. 121 miles

You might be interested in
There are 74 children at a camp 38 are girls the rest are boys how many boys are at the camp
True [87]

Answer:

36 boys are at the camp

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
What is the circumference of the circle? d=44in​
julsineya [31]

Answer:

138.23 in

hope this helps

have a good day :)

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
Gabby is buying flowers for a friend. She can choose daisies, carnations, or sunflowers. She can put the flowers in a clear, red
In-s [12.5K]

Answer:

Daisies: Clear vase

Carnations: Red vase

Sunflowers: Blue vase

Step-by-step explanation:

Your using all the objects and is is in all the combinations.

8 0
3 years ago
Read 2 more answers
8k + 2m = 3m + k<br><br> Solve for k
mina [271]
Minus both sides by 2m
8k = 3 m - 2m + k \\ 8k = m + k
Minus both sides by k
7k = m
Divided both sides by 7
k =  \frac{m}{7}
6 0
3 years ago
mr.torres is 6 1/4 feet tall. Mr. torres is 5 1/2 feet tall. How much shorter is Mrs. torres than her husband PLEASE HURRY!
OleMash [197]

Answer: 3/4

Step-by-step explanation: 6 1/4 - 5 1/2

7 0
3 years ago
Read 2 more answers
Other questions:
  • I need help in Adv. Math
    5·1 answer
  • Suppose there is a 13.4 % probability that a randomly selected person aged 30 years or older is a jogger. In​ addition, there is
    15·1 answer
  • Find the absolute maximum and absolute minimum values of f on the given interval.
    9·1 answer
  • Part B
    7·1 answer
  • HELP HELP PLEASE!!!!<br> Will give what ever u want
    13·1 answer
  • What is 9-h divided by 1/8; h = 1/3
    12·1 answer
  • Work out<br> 8^1/3 / 5^-2
    7·1 answer
  • Exsplain how to use a number line to show that opposite quantities combine to make 0.
    10·1 answer
  • 26t7abtrand sa b-7 soln​
    13·1 answer
  • 13 divided by 1209 please help
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!