A boat heading out to sea starts out at Point AA, at a horizontal distance of 968 feet from a lighthouse/the shore. From that point, the boat’s crew measures the angle of elevation to the lighthouse’s beacon-light from that point to be 7^{\circ} ∘ . At some later time, the crew measures the angle of elevation from point BB to be 3^{\circ} ∘ . Find the distance from point AA to point BB. Round your answer to the nearest tenth of a foot if necessary.

Answers

Answer 1

As the distance from the lighthouse, LH, increases, the angle of elevation,

reduces.

The distance from point A to point B is approximately 1,269.9 feet.

Reasons:

The distance of point A from the light house = 968 feet

Angle of elevation from point A to the lighthouse =

Angle of elevation from point B to the lighthouse =

Required:

The distance from point A to point B.

Solution:

[tex]\displaystyle tan(\theta) = \frac{Opposite \, side \, to\, angle}{Adjacent\, side \, to\, angle} = \mathbf{\frac{Height \ from \ sea \ to \ the \ light \ house }{Horizontal \ from \ boat \ to \ the\ LH}}[/tex]

Which gives;

[tex]\displaystyle tan(7^{\circ}) = \mathbf{\frac{Height \ from \ sea \ to \ the \ light \ house }{968 \ feet}}[/tex]

Height to the lighthouse = tan(7°) × 968 feet  ≈ 118.86 feet

From point B, we have;

[tex]\displaystyle tan(3^{\circ}) = \mathbf{ \frac{118.86 \ feet }{Horizontal \ distance \ from \ point \ B\ to \ LH}}[/tex]

Therefore;

[tex]\displaystyle Horizontal \ distance \ from \ boat \ to \ LH = \frac{118.86 \ feet }{tan(3^{\circ})} \approx \mathbf{2237.9 \, feet}[/tex]

Therefore;

Distance from A to B = D

D = Horizontal distance from B to LH - Horizontal distance from A to LH

Distance from A to B = 2237.9 feet - 968 feet ≈ 1269.9 feet

The distance from point A to point B, D ≈ 1,269.9 feet

Learn more about trigonometric ratios here:

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Related Questions

The total number of gallons of water in a tank, w, after t minutes is given in the table and the graph below. What is an equation showing the relationship between w and t? A. w = 2t B. w = 2 + t C. w = 4t D. w = 4 + t

Answers

Answer:

C. w = 4t

Step-by-step explanation:

Let's examine the way t and w are related to each other, one point at a time starting with (0, 0). This point really doesn't tell us much, but we do know that this relationship must be proportional since any line that goes through the origin (the point (0, 0)) is proportional. we can rule out B. 2 + t and D. 4 + t since neither of these go through the origin. 2 + t goes through the point (0, 2) and 4 + t goes through the point (0, 4).

Now, we have two options left: A. w = 2t and C. w = 4t. Which one is correct? Well, let's look at the point (1, 4). 1 × 2 is not equal to 4, but 1 × 4 is equal to 4, so C. w = 4t must be the correct option.

We can test this on the rest of the points as well: 2 × 4 = 8 and 3 × 4 = 12. Hopefully that's helpful! If you have questions or need clarification on anything, let me know. :)

Use the diagonals to determine whether a parallelogram with vertices A(2, 7), B(7, 9), C(5, 4), and D(0, 2) is a rectangle, rhombus, or square. Give all the names that apply.

Answers

Step-by-step explanation:

A and B have among each other the same distance relation as D and C : +5 in x, and +2 in y direction

and D and A have among each other the same distance relation as C and B : +2 in x, and +5 in y direction.

that means the slope of the first pair of sides is 2/5, and the slope of the second pair of sides is 5/2.

and that means that these 2 pairs of lines are not perpendicular (for this not only would we need to have the ratio upside down but also the sign would need to be flipped). there are no 90° angles.

so, there is no rectangle or square.

but because the sums of x and y coordinate differences are the same, we have the same distances between neighboring points.

and that makes it a rhombus.

Greg buys a school lunch for $1.50 each day. His caretaker gave him $40 for his lunches. What equation represents how much money Greg has?

Answers

Answer:

1.50 + 40= $41.50

Step-by-step explanation:

if Greg only had $1.50 and then he got an additional $40, he now has $41.50.

The Appalachian Trail is about 2,175 miles long.

a. If Katia averages 18 miles each day, how long will it take her to hike the length of the trail?

b. Katia’s friend Joelle joins her for the last quarter portion of the hike. How many full days will Joelle hike?

PLZ HELP I WILL GIVE BRAINLIEST TO WHOEVER ANSWERS THIS QUESTION!

Answers

Answer:

121 days; 30 full days

Step-by-step explanation:

to find how much days she takes you divide 2175 by 18

2175 / 18 is 120.833333

it will take her at least 121 days because you need to round up

the last portion of the hike would be a quarter of the hike

you would divide the final time by 4 and that is your answer

121 / 4 is 30.25

you have to round down because .25 is not a full day

she hiked 30 full days

1 1/3 x 5/8

A.3/4
B.4/5
C.5/6
D.5/8

Answers

the answer is 5/6, hope this helps
4/3 x 5/8 = 20/24 = 5/6

The answer is C.

How i can answer this question

Answers

Answer:

Your correct Awnsers are A and D

It’s for sure A for one but not sure on the second!

The population proportion for a certain characteristic is 0.28. In a sample of
100 people, 25 had that characteristic.
Which equation correctly describes the point estimate?
A. P = 0.28
B. p = 0.28
O c. p = 0.25
D. p = 0.25

Answers

Answer:

B. p= 0.25

Step-by-step explanation:

Pls give brainliest if helps

this question


please help please

m=n+4b

Answers

Answer:

m=n+4b:- b=m-n/4.........

6m+7n+5m−3n simpified

Answers

Answer:

11m + 4n

Step-by-step explanation:

when two numbers with the same variable are added together or subtracted the result is just the numbers added or subtracted. So you can add 6m and 5m to get 11m. and you can subtract 3n from 7n to get 4n

11m + 4n

A pole 12 feet tall is used to support a guy wire for a tower, which runs from the tower to a metal stake in the ground. After placing the pole, Moussa measures the distance from the pole to the stake and from the pole to the tower. Find the length of the guy wire, to the nearest foot.

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Answer: The answer is 189 ft.

in need of help. plz ​

Answers

The maximum degrees in a hexagon is 720 so minus all of the values you see on the screen to 720

(1 pc
3. A recipe calls for 4 cups of sugar to make 4 dozen cookies. Use the proportion to calculate
how much sugar is needed to make 8 dozen cookies.
4 cups
x cups
4 dozen 8 dozen
O2 cups
08 cups
08.5 cups
0 12 cups
I really need help! I give Brainly-est

Answers

Answer:

8cups

Step-by-step explanation:

if it takes 4-cups for 4-dozen. That's 1-cup each dozen so 8-dozen is 8-cups

What is the equation of this graphed line?
Enter your answer in slope-intercept form in the box.

Answers

Answer:

y = -1/3x - 5

Introduction:

The slope intercept form of a line is y = mx + b. Now, let's start out by solving the slope.

Step-by step explanation:

=> Slope = rise/run = [tex]\frac{y_{2} - y_{1} }{x_{2}-x_{1} }[/tex]=> Slope = [tex]\frac{-3- (-7) }{-6-6 }[/tex]=> Slope = [tex]\frac{4}{-12}[/tex]=> Slope = [tex]\frac{-1}{3}[/tex]

Since we have found the slope, let's find the y-intercept to create our equation.

=> y-intercept = -5

Conclusion:

Therefore, our new equation is y = -1/3x - 5

Hoped this helped.

[tex]BrainiacUser1357[/tex]

Please help me 87x89 PLEASE

Answers

The answer to 87x89 is 7,743.

Answer:

7743 :)

Step-by-step explanation:

The graph of y = f(x) is the solid black graph below. Which function represents the
dotted graph?
Submit Answer
O y = f(x + 3) - 5
O y = f(x - 3) - 5
O y = f(x - 3) + 5
O y = f(x + 3) + 5

Answers

Answer:First option, y=f(x+3)+5

Step-by-step explanation:

analyse the transformation first

From the dotted function, when compared to the solid black line, is moved 3 units to the left, and moved upwards by 5 units

Input transformation

In graphing, when a value is shifted horizontally, its transformation is equal to: -(x2-x1), and in this instance, we end up with a value of +3so, f(x+3) is the first componentWhen a function is shifted horizontally, it is proportiante to the distance it moves, so (y2-y1)in this instance, it is 0 - -5=5so the transformation vertically is +5

Final answer, when all values are added is y=f(x+3)+5

IMPORTANT QUESTION: If i have 464 assignments to do, and want to get it done in 130 days how many assignments should I do a day?

Answers

Answer:

4 assignments per day.

Step-by-step explanation:

Since you have 464 assignments, and 130 days, then you can divide.464/130 = 3  37/65Since you have a fraction, you can round it to 4 assignments.

Answer:

3 .

Step-by-step explanation:

464 / 130

it’s not exactly like this,

if Im wrong!

suppose+the+population+of+a+small+town+is+16000+and+growing+exponentially+at+2.2+%.+how+many+years+until+the+population+reaches+25000?

Answers

Answer:

  20.5 years

Step-by-step explanation:

The population is given by the exponential function ...

  p = 16000·(1 +0.022)^t

When p = 25000, we can find the value of t by taking logarithms.

  log(25000/16000) = t·log(1.022) . . . . . divide by 16000, take the log

  t = log(25/16)/log(1.022) ≈ 20.5 . . . . . . divide by the coefficient of t

It will take about 20.5 years for the population to reach 25000.

15 POINTS HELP PLZ

Which expression is equal to f(x) - g(x)?

Answers

Answer:

c it's probably c I think I'm not really too good at this but I'm probably sure it's c.


Find the inequality represented by the graph.

Answers

Answer:

y ≤ -1/3x + 1

Step-by-step explanation:

find the slope and y-intercept and write equation in form of

y = mx + b;  m = slope and b = y-intercept

if you start at (0,1) and move down and to the right to (3,0) you get a slope equal to -1/3

we can see by looking at the graph that the y-intercept is 1

therefore, y ≤ -1/3x + 1

Determine whether the following pairs of lines are parallel, perpendicular, or neither. y=1/3x+4 3x+y=2​

Answers

Answer:

parallel

Step-by-step explanation:

Answer:

The lines are perpendicular

Step-by-step explanation:

Y=1/3x+4

Y=-3x+2

The negative reciprocal of -3 is 1/3

ASAP HELP Can a triangle have sides with the given lengths? Explain, showing all the work
8 ft, 9 ft, 18 ft
PLEASE EXPLAIN

Answers

Answer:

Yes

Step-by-step explanation:

the triangle is a scalene triangle (has no equal parts

find the domain of y=1/2 square root of x+2-3

Answers

35 ——————————————————

Miss Watson runs a distance of 200 meters in 25 seconds.
Work out the average speed of Miss Watson in meters per second?

Answers

Step-by-step explanation:

D = 200m T = 25s

The formula for speed is speed = distance ÷ time

S = 200 ÷ 25

S = 8m/s

Please Help Question in picture

Also could you drop your socials so I can ask a few more questions through dm's im running low on brainly points

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Answer:

the coordinates of B are; (7,3)

534 divided by 43. Please help..

Answers

Answer:

Step-by-step explanation:

The numbers in the fraction cannot be reduced to create a simplified fraction. Therefore there are 3 ways to write this answer ...

1) [tex]\frac{534}{43}[/tex]

2) 12[tex]\frac{18}{43}[/tex]

3) 12.41861

Which of the following is the rational exponent expression of 4 square root of f?
OF
Of4
O4f
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Answers

the answer is A f1/4

The graph shows a proportional relationship between the number of books sold at a yard sale and the amount of money collected from book sales.

Answers

Answer:

1.5

Step-by-step explanation:

6/4

I will give these ponts for free if u answer 100+100x100. (help me get brnliest)

Answers

In the beginning operations are performed with multiplication,,,so
100x100=10.000+100=
10.100result…

Answer:

10,100

Step-by-step explanation:

100*100=10000+100=10,000

PLEASE HELP ME!!! I"L GIVE BRAINLEST


3m + 3

m = -7

-12

-18

-16

24

Answers

Answer:

m = [tex]\frac{-421}{6}[/tex]

Step-by-step explanation:

Let's solve your equation step-by-step.

x

Step 1: Simplify both sides of the equation.

3m+3m=−7−12−18−(16)x(24)

3m+3m=−7+−12+−18+(−384)

(3m+3m)=(−7+−12+−18+(−384))(Combine Like Terms)

6m=−421

6m=−421

Step 2: Divide both sides by 6.

[tex]\frac{6m}{6} =\frac{-421}{6}[/tex]

m = [tex]\frac{-421}{6}[/tex]

I really hope this help's :)

what is g(5)?
g(x)=−x+4, find g(5)

Answers

Answer:

g(5) = -1

Step-by-step explanation:

g(5)= -(5)+4

g(5)= -1

g(x) = -x + 4Putting x = 5, we getg(5) = -5 + 4or, g (5) = -1

Answer:

-1

Hope you could get an idea from here.

Doubt clarification - use comment section.

꧁TheoriesMadeTheWorld꧂

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