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
Fynjy0 [20]
3 years ago
14

A fisherman leaves his home port and heads in the direction N 70 ° W. He travels d1 = 40 mi and reaches Egg Island. The next day

he sails N 10 ° E for d2 = 65 mi, reaching Forrest Island.
(a) Find the distance between the fisherman's home port and Forrest Island. (Round your answer to two decimal places.)
(b) Find the bearing from Forrest Island back to his home port. (Round your answer to one decimal place.)
S ° E

Mathematics
1 answer:
Gnesinka [82]3 years ago
4 0

Answer:

A)82.02 mi

B) 18.7° SE

Step-by-step explanation:

From the image attached, we can see the angles and distance depicted as given in the question. Using parallel angles, we have been able to establish that the internal angle at egg island is 100°.

A) Thus, we can find the distance between the home port and forrest island using law of cosines which is that;

a² = b² + c² - 2bc Cos A

Thus, let the distance between the home port and forrest island be x.

So,

x² = 40² + 65² - 2(40 × 65)cos 100

x² = 1600 + 4225 - (2 × 2600 × -0.1736)

x² = 6727.72

x = √6727.72

x = 82.02 mi

B) To find the bearing from Forrest Island back to his home port, we will make use of law of sines which is that;

A/sinA = b/sinB = c/sinC

82.02/sin 100 = 40/sinθ

Cross multiply to get;

sinθ = (40 × sin 100)/82.02

sin θ = 0.4803

θ = sin^(-1) 0.4803

θ = 28.7°

From the diagram we can see that from parallel angles, 10° is part of the total angle θ.

Thus, the bearing from Forrest Island back to his home port is;

28.7 - 10 = 18.7° SE

You might be interested in
Solve and show your work for each question a). B). C).
Andreyy89

Answer:

Step-by-step explanation:

a) Here, the first term is .48 and the common ratio is 1/100 (since each new 48 is 1/100 th of the previous 48).                                   a

Use the formula s = sum of geometric series = -----------

                                                                                  1 - r

                                           0.48              48

which in this case is s = --------------- = ------------ = 48/99 = 16/33

                                          1 - 1/100        100 - 1

Check this result by finding 16/33 on a calculator.  Is the result equal to 0.484848484848.... ?  Yes

b) Here we have the bar over the 8 only.  0.48 with the bar over the 8 is equivalent to 0.4888888888 ...

                                                              0.08

or 0.4 + 0.0888888888 ...      or 0.4 + ------------

                                                                1 - 1/10

                                             

                                              0.08                       8

and this simplifies to 0.4 + ------------  =  0.4 + ---------

                                                9/10                      90

Evaluating this last result on a calculator results in 0.488888888 ...

c)  0.48 expressed as a fraction is  48/100 = 12/25

6 0
3 years ago
What is 20x12? please help! thankss!!
Vanyuwa [196]
240 is the correct answer. 
6 0
3 years ago
Read 2 more answers
Maggie wants to know how many students in her school enjoy watching sports on TV. She asks all 25 students in her math class and
RSB [31]
No, it is not a valid inference because her classmates do not make up a random sample of the students in the school.
6 0
3 years ago
Read 2 more answers
Sum of three numbers in an as is 33 and the sum of thier cubes is 5049.find the numbers
Alex73 [517]

Sum of three numbers is 33 and  sum of their cubes is 5049 then three numbers are 7,11,15 or 15,11,7.

As given,

Let a-d, a, a +d be three numbers

Sum =33

⇒a-d + a +a +d =33

⇒ a =11

Sum of cubes= 5049

⇒ (a-d)³ + a +(a +d)³ =5049

⇒ a³ -d³ -3a²d +3ad² + a³ +a³ +d³ +3a²d +3ad² =5049

⇒3a³ + 6ad² = 5049

⇒ d=± 4

Therefore, sum of three numbers is 33 and  sum of their cubes is 5049 then three numbers are 7,11,15 or 15,11,7.

Learn more about numbers here

brainly.com/question/17429689

#SPJ4

6 0
1 year ago
What is the diagonal distance across a rectangular yard that is 20 yd by 48yd
garik1379 [7]
Use Pythagorean Theorem

C2 = a2 + b2
c2 = 20^2 + 48^2
c2 = 400 + 2304
c2 = 2704
c = 52
5 0
3 years ago
Other questions:
  • If a student had homework 87 days out of 100 what fraction and what percentage of days did the student not have homework? Give 2
    14·2 answers
  • How do you solve -7 times -3/5 times 15/7
    15·1 answer
  • 10 POINTS AND BRAINLIEST! PLEASE ANSWER BOTH QUESTIONS!
    7·1 answer
  • Find 1/8 of 12. Express your answer in simplest form.<br> 1 1/2<br> 2/3<br> 1/96<br> 12/8
    11·2 answers
  • If 2x+y=12 and x+2y=-6 what is the value of 2x+2y
    10·1 answer
  • How do you factor x²-100 ?
    9·1 answer
  • Pls help me if u can
    7·1 answer
  • Write the equation of the perpendicular line with the points (-9,2) with the equation 3x-y=12
    10·1 answer
  • how do you put 100,000 years in word form? (like a century, decade, millennium, etc) I will give you branliest answer if you can
    6·2 answers
  • I need help please......
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!