A helicopter flies between two islands that are 20 miles apart. The angle of elevation with one island is 15o and 35o with the second island. What is the mileage of the helicopter? Round your answer to the nearest tenth of a mile. (Law of Sines or Law of Cosines Problem)
Answers
Answer:
Step-by-step explanation:
From the figure attached,
A helicopter is flying at a height 'h' and angle of elevations from two islands C and B are 35° and 15° respectively.
Let the measure of BD = x miles
From ΔABD,
tan(15) = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}=\frac{h}{x}[/tex]
h = x.tan(15) ---------(1)
From ΔACD,
tan(35) = [tex]\frac{h}{12-x}[/tex]
h = (12 - x).tan(35) ------(2)
By equating the values of h from equations (1) and (2),
x.tan(15) = (12 - x).tan(35)
[tex]\frac{x}{12-x}=\frac{\text{tan}35}{\text{tan}15}[/tex]
[tex]\frac{x}{12-x}=2.613[/tex]
x = 2.613(12 - x)
x + 2.613x = 31.386
3.613x = 31.386
x = 9.914 ≈ 9.9 miles
From equation (1),
h = x.tan(15)
= 9.9[tan(15)]
= 2.65 ≈ 2.7 miles
Therefore, helicopter is flying at the vertical height = 2.7 miles and horizontal distance of the helicopter from the island B = 9.9 miles.
Answer:
2.7
Step-by-step explanation:
I took the quiz and got it right :)
Related Questions
The figure shows Triangle ABC and some of its transformed images on a coordinate grid:
Which of the four triangles was formed by a translation of Triangle ABC? (4 points)
3
2
0 1
04
Answers
Answer:
2
Step-by-step explanation:
it is congruent
1. One complete sentence about rotations.
Answers
Answer: The Earth makes one rotation every day.
Step-by-step explanation:
Find the coordinate of the midpoint of GH with endpoints G(-5,4) and H (-5,8)
Answers
Answer:
(-5,6)
Step-by-step explanation:
G(-5,4)=(x1,y1)
H(-5,8)=(x2, y2)
midpoint=?
now,
(x,y)= x1+x2/2 y1+y2/2
-5-5/2 4+8/2
-10/2 12/2
-5 6
therefore the co ordinates of midpoint are(-5,6)
Can anyone give the answer for the question which i have attached .
Answers
3(a - 1) + 2a = a + 1
Answers
Answer:
a = 1
Step-by-step explanation:
Step 1: Write equation
3(a - 1) + 2a = a + 1
Step 2: Solve for a
Distribute 3: 3a - 3 + 2a = a + 1
Combine like terms: 5a - 3 = a + 1
Subtract a on both sides: 4a - 3 = 1
Add 3 on both sides: 4a = 4
Divide both sides by 4: a = 1
Solve the following inequality: 9x+2/3(−7x+6)−1≥2
Answers
Answer:
Step-by-step explanation:
3(9x - 14/3x + 4 - 1 ≥ 2)
27x - 14x + 12 - 3 ≥ 6
13x + 9 ≥ 6
13x ≥ -3
x ≥ -3/13
Answer:
x ≥ - [tex]\frac{3}{13}[/tex]
Step-by-step explanation:
Given
9x + [tex]\frac{2}{3}[/tex](- 7x + 6) - 1 ≥ 2
Multiply through by 3 to clear the fraction
27x + 2(- 7x + 6) - 3 ≥ 6 ← distribute and simplify left side
27x - 14x + 12 - 3 ≥ 6
13x + 9 ≥ 6 ( subtract 9 from both sides )
13x ≥ - 3 ( divide both sides by 13 )
x ≥ - [tex]\frac{3}{13}[/tex]
use a straightedge and a compass to construct a segment of length AB+CD
Answers
Answer:
I also just noticed that is saying construct a segment of the lenght of both of them so after you have both lenght measure them draw AB close point get CD and trace it over start from B and there you have the big segment which is made of both of them AB + CD
:)
Step-by-step explanation:
So basically get your compass and start by these steps
first get the total lenght of AB lets say its 100
when you go to make CD angle all you have to do
its trace same line and there you got both points same sizes
I hope that helped.
Solve the following system of equations using the elimination method. 2x + 4y = 10 –2x + y = –15
Answers
Answer:
(7, - 1 )
Step-by-step explanation:
Given the 2 equations
2x + 4y = 10 → (1)
- 2x + y = - 15 → (2)
Adding the 2 equations term by term eliminates the term in x, that is
5y = - 5 ( divide both sides by 5 )
y = - 1
Substitute y = - 1 into either of the 2 equations and solve for x
Substituting into (1)
2x + 4(- 1) = 10
2x - 4 = 10 ( add 4 to both sides )
2x = 14 ( divide both sides by 2 )
x = 7
Solution is (7, - 1 )
(7, - 1 )
Step-by-step explanation:
Given the 2 equations
2x + 4y = 10 → (1)
- 2x + y = - 15 → (2)
Adding the 2 equations term by term eliminates the term in x, that is
5y = - 5 ( divide both sides by 5 )
y = - 1
Substitute y = - 1 into either of the 2 equations and solve for x
Substituting into (1)
2x + 4(- 1) = 10
2x - 4 = 10 ( add 4 to both sides )
2x = 14 ( divide both sides by 2 )
x = 7
Solution is (7, - 1 )
What type of quantity is momentum? (2 points)
It is a scalar quantity because it involves magnitude only.
It is a vector quantity because it involves magnitude only.
It is a scalar quantity because it involves magnitude and direction.
It is a vector quantity because it involves magnitude and direction.
Answers
Answer:
it is a scalar quantity because it involves magnitude only.
Step-by-step explanation:
(5,0) is a solution to the equation y = 5x + 5 Question 11 options: True False
Answers
Answer:
False
Step-by-step explanation:
y=5x + 5
0=5 (5)+5
0=10+5
0≠15
False
Given the table, what is the common difference in the elevation of the scuba diver?
Answers
Answer:
the common difference is that it's taking away 4 or -4
what is the y-intercept of the table shown?
Answers
Answer:
the answer is (0,-2) trust bro I did the work
Name a pair of vertical angles (there may be more than one choice)
<1 and <4
<1 and <2
<2 and <4
<2 and <5
<5 and <4
Answers
Jorge walks 1 mile in 1 hour. In 2 hours at the same pace, Jorge can walk ____ yards.
Answers
Answer:
.
Step-by-step explanation:
Can someone help me solve this? ^^
Answers
Answer to a.
a. −14/15
The correlation coefficient r between an employee’s age, x, and yearly salary, y, is 0.633. What percent of the variation in yearly salaries can be explained by differences in the employees’ ages? 31.7% 63.3% 15.8% 40.1%
Answers
Answer:
The answer is 40.1%
Step-by-step explanation:
I just took the test
The variation in the yearly salaries can be explained by the differences in employee ages up to 40.1%.
When given the correlation coefficient of two variables, you can find out how much of the variation in the dependent variable can be explained by the independent variable by the formula:
= (Correlation coefficient)² x 100%
= 0.633² x 100%
= 0.4007 x 100%
= 40.1%
In conclusion, 40.1% of the variation in salary can be explained by age.
Find out more at https://brainly.com/question/3560028.
If T is the midpoint of SU, what are ST, TU, and SU.
*Question 16*
Answers
We have ST=5x, TU=3x+32 and they're equal if T is the midpoint:
5x = 3x + 32
2x = 32
x = 16
ST = 5x = 80
So TU = 80 and SU=160
Answer: Second choice
Rearrange the variables to write the equation, LaTeX: V=\frac{8T}{P}
V
=
8
T
P
, to solve for temperature, T, as a function of volume and pressure, V and P. Write out your work on paper and submit a picture.
Answers
Answer:
T = VP/8Step-by-step explanation:
Given formula
V = 8T/PSolving for T
V = 8T/P ⇒ multiply both sides by TVP= 8T ⇒ divide both sides by 8VP/8 = TT = VP/8 ⇒ answerSam and James needed a midnight snack. They found
a cake that Sam's mom had just made that day. Sam
and James were the first to eat the cake. If Sam ate
2s of the cake and James ate of the cake, how
much of the cake was left?
Answers
Answer:
if the cake was full the slices remined were four
What is the factored form of x6 - 9?
Answers
What is the value of x in the figure below? In this diagram, AABD - ACAD
Answers
Answer:
E. √39Step-by-step explanation:
see attached
From the similar triangles value of x is √39. Therefore, option E is the correct answer.
From the given triangle, CD=13, BD=3 and AD=x.
Given that, ΔABD is similar to ΔCAD.
CD/AD = AD/BD
13/AD = AD/3
39 = AD²
AD = √39 = x
Therefore, option E is the correct answer.
To learn more about the similar triangles visit:
https://brainly.com/question/25882965.
#SPJ7
yesterday 15 degrees below zero. Write an integer to represent this temperature.
Answers
Answer:
-15
I hope this helped! :)
4+(9x2)÷(4-1)-4 simplify by using order of operations
Answers
Answer:
the answer is 6 just do the math and it's pretty easy
Steps to solve:
4 + (9 * 2) / (4 - 1) - 4
~Simplify what is in parenthesis
4 + (18) / (3) - 4
~Divide
4 + 6 - 4
~Add
10 - 4
~Subtract
6
Best of Luck!
Chapters: 1.Integers
Answer the following questions:
1. Complete the pattern:
a) 8,3, -2, -7,
b) 20, 12, 4,
c) -14, -10, -6,
Answers
Answer:
a) -12
b) -4
c)-2
Step-by-step explanation:
a) pattern is minus 5
b) pattern is minus 8
c) pattern is plus 4
4. Asma can iron 5 shirts in 14 minutes. How long will she take to iron 35 shirts?
n make a water tank emnty in 20 minutes. But 2 pumps are
Answers
Answer:
Asma can iron 5 shirts in 14 minutes.
She can iron 1 shirt in 14/5 minutes.
she can iron 35 shirts in (14/5)×35 minutes.
=98 minutes i.e1 hour 38 minutes
Sara has $1.30 less than double what Billy does. Sara has $53.72. How much money does Billy have?
Answers
Answer:
Billy has $27.51
Step-by-step explanation:
First let's set up an equation to solve this problem.
Assign a variable to Billy's amount. Let's make it x.
Then we just interpret the problem and solve:
2x - 1.30 = 53.72
+1.30 +1.30
----------------------------
2x = 55.02
(Divide by 2 on both sides)
----------------------------
x = $27.51
2x = Billy's amount doubled
2x - 1.30 = Taking away 1.30 from double Billy's amount
53.72 = Sara's amount
New York City has a population of 8.55 million and 300 square mile. Manhattan has 1.64 million and 23 square miles. How much greater is the population of Manhattan than New York City?
Answers
Given :
New York City has a population of 8.55 million and 300 square mile area .
Manhattan has 1.64 million and 23 square miles area .
To Find :
How much greater is the population density of Manhattan than New York City.
Solution :
Population density of New York City :
[tex]D_{NY}=\dfrac{8.55}{300}=0.029 \ million/mile^2\\\\D_{M}=\dfrac{1.64}{23}=0.071 \ million/mile^2[/tex]
Now ,
[tex]D_{M}-D_{NY}\\\\(0.071-0.029)=0.042\ million/miles^2[/tex]
Therefore , population density of Manhattan is [tex]0.042\ million/miles^2[/tex] greater than New York City .
Hence , this is the required solution .
18. Solve the equation.
m- 10/3 - 5m-9/7 = 1
Answers
The answer is m = -59/42
Step by step explanation is in the image below.
What are each step in the process for solving an equation
Answers
Answer:
1. Simplify each side of the equation by removing parentheses and combining like terms.
2. Use addition or subtraction to isolate the variable term on one side of the equation.
3. Use multiplication or division to solve for the variable.
3[7x - 4(x - 3)] + 1
Answers
Answer:
9x+37
Step-by-step explanation:
Answer:
9x + 37
Step-by-step explanation:
3[7x - 4(x - 3)] + 1
3[7x-4x+12] + 1
3[3x +12] +1
9x + 36 +1
9x + 37