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]
3 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]3 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]3 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
A juice recipe calls for 5 cups of grape juice for every 2 cups of peach juice are needed for a batch that uses 8 cups of peach
Ksivusya [100]

Answer: 20 cups of grape juice are needed for 8 cups of peach juice.

Step-by-step explanation:

5 times 4 is 20.

We must do this step because you need 2 cups for 1 batch, and times 4 that is 8. So then we multiplied 5 times 4.

So, 20 cups of grape juice are needed for 8 cups of peach juice.

Hope this answer helps you out!

3 0
3 years ago
Read 2 more answers
Solve for x and explain how I show work
DaniilM [7]

Answer:

x = 100

Step-by-step explanation:

(x - 20) + x = 180  

2x - 20 = 180

<u>    + 20    +20</u>

2x = 200

x = 200/2

x = 100

3 0
2 years ago
Identify the range of the function
NeX [460]

Answer:

what function

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
A candy bar is rectangular in shape and measures 3 inches by 4 inches by .5 inches. How many of the candy bars will fit into the
allsm [11]
It will fit 17 candy bars. Hope this helps!
4 0
3 years ago
On a coordinate grid, a park is located at (3,0) and the pool is located at (-3,3). If the tennis courts are the midpoint betwee
Lemur [1.5K]

I think c if not sorry have a good day

7 0
3 years ago
Read 2 more answers
Other questions:
  • Find the height of a rectangular prism if the volume is 171 in, the length is 6 in, and the width is 4 3/4.
    15·2 answers
  • Emilie rides her bike x miles be for eshe gets a flat tire. She walks 1/3 mile to a bus stop and then takes a bus for 2 1/2 mile
    5·2 answers
  • What is the answer to this 8-(-8)=
    8·2 answers
  • Use the distributive property to simplify the expression. -7(8x-3)+x
    9·2 answers
  • Find the value of 3v- 10 given that 2v- 7 = 9
    8·2 answers
  • Simplify the expression: 6 + 3(x + 4)
    15·2 answers
  • Determine the domain and range for each of the following:
    14·1 answer
  • On a number line, which value is closest to zero?
    13·2 answers
  • Please help me thank you so much
    13·1 answer
  • Can i have help with this question please i don’t understand
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!