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
How do you write 999.9% as a decimal?
Hoochie [10]

Answer:

9.999

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
The difference of 28 and a number m is 3
jonny [76]

Answer:

28 - m = 3

28 - 3 = m

25 = m

Hope this helps :) mark me brainliest if you want to

8 0
2 years ago
Why would my teacher give me a math paper on something I didn't learn yet? Is she okay?
luda_lava [24]

Answer:

your teacher is crazy about she think you are smart

5 0
2 years ago
Read 2 more answers
What is the length of a rectangle with an area of 48 yd squared, and a width of 3 yd
Leona [35]
The length of the rectangle is 16.
7 0
3 years ago
Read 2 more answers
How can 8 students share a pizza cut into 12 slices without cutting any of the slices?
Triss [41]
Hmmm...
We have to divide 12 by 8, since we need to see how 8 students will share 12 slices.

12/8=1 and 1/2

So, each student can have a slice and a half, but since we aren't allowed to cut the slices...

We can let each student have one slice, with 4 left over, so...

Every student can have one slice, and then half can have a second slice :)!

I'm not sure if that is what was meant by the question, but that was all I could think of.

I hope I helped! :)
3 0
3 years ago
Other questions:
  • Two gears are connected and are rotating simultaneously. The smaller gear has a radius of 2 inches, and the larger gear has a ra
    5·1 answer
  • Write the expression that shows " 3 times the sixth power of 10."
    11·1 answer
  • What is the value of w <br><br> W+33=2W
    13·1 answer
  • Which of the following describes a simple event?
    15·2 answers
  • Product of two negative factors
    6·2 answers
  • You meet with the financial aid office to discuss your costs for attending MGA next semester. Tuition is
    5·1 answer
  • Plz Help...What is the square root of 1,249?
    11·1 answer
  • The where sells bagels zero $.75 each the bagel shop sells one dozen for seven dollars which is the better buy
    9·1 answer
  • WILL GIVE 100 POINTS
    5·2 answers
  • A bag contains nine yellow marbles and nine red marbles. You randomly select two marbles from the bag. What is the probability t
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!