A boat is heading towards a lighthouse, where Riley is watching from a vertical distance of 120 feet above the water. Riley measures an angle of depression to the boat at point A to be 18 degrees . At some later time , Riley takes another measurement and finds the angle of depression to the boat (now at point B) to be 65 degrees . Find the distance from point A to point B. Round your answer to the nearest foot if necessary .

Answers

Answer 1

Answer:

313 ft

Step-by-step explanation:

It's hard to explain because its geometry, but there will be a right triangle with angle of 72 and another with angle of 25. do tan72 * 120 - tan25 * 120

Answer 2

The distance from point A to point B is given by the trigonometric relations and d = 313 feet

What are trigonometric relations?

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

tan θ = sin θ / cos θ

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

Given data ,

Let the first triangle be represented as ΔAOD

Let the second triangle be represented as ΔBOD

where the distance from point A to point B = d

And , Riley is watching from a vertical distance of 120 feet above the water

Riley measures an angle of depression to the boat at point A to be 18 degrees

Riley takes another measurement and finds the angle of depression to the boat (now at point B) to be 65 degrees

So , ∠BOD = 25° and ∠AOD = 72°

From the trigonometric relations ,

tan θ = opposite / adjacent

tan AOD = AD / OD = tan 72°

tan 72° = 3.087

tan BOD = tan 25° = 0.47

Now , the measure of AD = 120 x 3.087 = 369.6 feet

And , the measure of BD = 120 x 0.74 = 56.4 feet

Therefore , the distance from A to B = 369.6 feet - 56.4 feet

d = 313 feet

Hence , the distance is 313 feet

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Related Questions

Find the equivalent exponential expression.
(4^2)4

Answers

Answer:

4^8

Step-by-step explanation:

If the second 4 is an exponent, as in (4^2)^4, then multiply the exponents.

(4^2)^4 = 4^(2 * 4) = 4^8

It is Keke’s birthday, and her parents want to surprise her with a room full of balloons. Use the Fermi process
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Answer:

im not sure sorry .

Step-by-step explanation:

If the circumference of a right cylinder is tripled, the volume will increase by a factor of _____.

Answers

Answer:the answer is 9

Step-by-step explanation:

A bag contains eight tiles labeled A, B, C, D, E, F, G, and H. One tile will be randomly picked.
What is the probability of picking a vowel?
Write your answer as a fraction.

Answers

Answer:

1/4

Step-by-step explanation:

Count all of the vowels (this will be your numerator):

A and E

2

Count all of the letters (this will be your denominator):

A, B, C, D, E, F, G, and H

8

Write this as a fraction:

2/8

Simplify:

2/8 = 1/4

please help!! this is geometry

Answers

Step-by-step explanation:

1 and 3 are complimentary angles, meaning 1+3 = 180 degrees.

in the same way 1 and 2 are complimentary angles, 1+2 = 180, => 2 ≈ 3

and for 2 and 4 the same => 1 ≈ 4

3 and 5 are complimentary angles, 3+5 = 180 degrees, => 1 ≈ 5.

7 and 8 are complimentary angles, 7+8 = 180 degrees, => (given that 1 ≈ 7 and therefore ≈ 4) 8 ≈ 2 ≈ 3

6 and 8 are complimentary angles, 6+8 = 180 degrees, => 6 ≈ 7 ≈ 1

and with 1≈5 and 1≈6 we know 5≈6.

A math teacher claims that the students' test scores are directly proportional to the amount of time spent studying. Amy studies 17 hours for a test and gets a score of 68. At this rate, how many hours would she have to study to get a score of 97?

Answers

Answer:

97/4 = 24.25 hours

Step-by-step explanation:

68 = 17x

x = 68/17 = 4

Using the graph, determine the equation of the axis of symmetry.​

Answers

Answer:

x = 6

Step-by-step explanation:

The axis of symmetry passes through the vertex of the graph

It is a vertical line with equation

x = c ( c is the x- coordinate of the vertex )

vertex = (6, 1 ) with x- coordinate 6 , then

equation of axis of symmetry is x = 6

HELP ME PLS I NEEDA GET THIS RIGHT PLS PLS ITS PYTHAGOREAN THEOREM

Answers

2.8 mm

2mm^2=4mm

4mm+4mm = 8mm

square root of 8mm is 2sqrt2

2sqrt 2 is 2.8 mm

Can someone help me on this math question its confusing ill give brainly when right!!!

Answers

Answer:

x=5

Step-by-step explanation:

x=[tex]\sqrt{25}[/tex]

x=5

Solve for x if 25'+ 3(5') = 4​

Answers

Answer:

x=0

Step-by-step explanation:

Let 5x = y.

(52)x+3(5x)−4=0

y2+3y−4=0

y2−y+4y−4=0

y(y−1)+4(y−1)=0

(y+4)(y−1)=0

y=−4;y=1

y = -4 is not possible.

y = 1 ⟹ x = 0.

Answer:

0

Step-by-step explanation:

Explanation:

HELP PLEASE!!
Which best describes the relationship between the lines
with equations -3x – 4y = 1 and -6x – 8y = 2?
A. Perpendicular
B. Neither perpendicular or parallel
C. Parallel
D. Same line

Answers

Answer:

same line

Step-by-step explanation:

its the exact same equation, but the second is multiplied by 2

Jenn starts out with $2000 in her bank account. On average, she spends $150 a week from her account. At that rate, how many weeks will it take her to run out of money?

Answers

Answer:

About 13 weeks

Step-by-step explanation:

Which of the following are valid probability distributions?

Answers

Answer:

Step-by-step explanation:

HELPPP

Which shapes have the greatest area?
(Select all that apply.)

Answers

Answer is 1st and 3rd shape

Whose area is 4 units

Answered by Gauthmath must click thanks and mark brainliest

the Marked price of a book is rupees 160 if it is sold at 15% discount find the discount amount and selling price​

Answers

answer is 15%

Step-by-step explanation:

cost prices of book =160

selling prices of book =136

now,rate of discount =loss% (as discount only leads to some kind of loss)

so CP>SP

so loss=CP-SP =160-136=24

loss%= (loss/CP)÷100

=(24/160)÷100

=15%

so rate of discount =15%

calculate the speed, in ms-¹ of vehicle A and of vehicle B​

Answers

9514 1404 393

Answer:

A: 0.32 m/sB: 0.56 m/s

Step-by-step explanation:

The speed is the ratio of the change in distance to the corresponding change in time.

Vehicle A moves from a position of 12 m to one of 28 m in 50 seconds, so its speed is ...

  A = (28 -12)/50 m/s = 16/50 m/s = 0.32 m/s

Vehicle B moves from 0 to 28 m in 50 seconds, so its speed is ...

  B = (28 m)/(50 s) = 0.56 m/s

simplify (4+√3)(4-√3)

Answers

Answer:

13

Step-by-step explanation:

(4+√3)(4-√3) = (4)^2-(√3)^2 =16-3 = 13

Answer:

Step-by-step explanation:

(a + b)(a -b) =a² - b²

a = 4 and  b = √3

(4 + √3)(4 - √3)= 4² - (√3)²

                        = 16 - √3*√3

                        = 16 - 3

                        =  13

If the campers at Camp Grilled Meat prefer hot dogs to hamburgers by a ratio of 4:3, and they need 500 hot dogs, how many hamburgers will they need?

Answers

Step-by-step explanation:

jsndmdmsmsnananansndbdbnd

Which graph represents a decreasing trend

Answers

Answer:

Excuse me! plz provide the graphs 2.

Solve A = 1/2bh for h

Answers

Answer:

2A /b = h

Step-by-step explanation:

A = 1/2 bh

Multiply each side by 2

2A = 2*1/2 bh

2A = bh

Divide each side by b

2A/b = bh/b

2A /b = h

Please show your work
[tex]1\frac{2}{3} + 2\frac{3}{4}[/tex]

Answers

Answer:

[tex]→1 \frac{2}{3} + 2 \frac{3}{4} \\ = \frac{5}{3} + \frac{11}{4} \\ = \frac{20 + 33}{12} \\ = \frac{53}{12}\\ =\boxed{4\frac{5}{12}}✓[/tex]

53/12 is the right answer.

Steps:

1 2/3 + 2 3/4 can also be written as...

5/3 + 11/4

The LCD is 12 so we make both fractions have a denominator of 12.

That gives us 20/12+33/12

Now you can add the numerators (but leave the denominator the same)

That gives us 53/12, but our simplified version would give us 4 5/12 as our final answer.

Answer:

[tex]4\frac{5}{12\\}[/tex]

Please mark brainliest if that helps!

The circumference of a circle is 16πw⁴.

Derive an expression for the area in terms of pi and w

Answers

Answer:

A = Pi (8 w**4)**2

Step-by-step explanation:

C = 16 Pi w**4 (given)

C = 2 Pi R (stand forula)

So then find R in terms of w by settting C = C from above

2 Pi r = 16 Pi w**4

2R = 16 w**4

R = 8 w**4

SO

A = Pi R**2

A = Pi (8 w**4)**2

a horizontally laid standard weight pipe has a diameter of 10 inches and is 12 feet long. The pipe is filled 9 inches high with water. How many gallons of water does the pipe hold? (Round your answer to the nearest gallon.) Please help.

Answers

Answer:

d isósceles hijo muy graciosa ya no me acuerdo de nada y tu q ases hablas con el

SEE QUESTION IN IMAGE

Answers

Answer:

Step-by-step explanation:

15) should be b) 6.7, 6 as the median is the average of the 25th and 26th result, these both occur in the 6 group and is the only option with a whole number for median

To check the mean

(2(4) + 7(5) + 17(6) + 10(7) + 8(8) + 6(9)) / 50 = 6.66 ≈ 6.7

16) mode is 1 child as the single largest grouping is 11 families

there were 46 families polled so the median occurs between 23 and 24

7 + 11 + 6 is 24 therefore median falls under 2 children.

a) 1, 2

14. Peter needs to buy a package of pencils to write his final exam. The store offers two packages.
Package 1: pack of 6 pencils for $1.68
Package 2: pack of 9 pencils for $2.34
Determine the cost per pencil. Which is the better deal? Round to 2 decimal places. Show all your work for full marks. (3 marks)

Answers

I dont think anyones gonna be helping you bud Ill repost the question for you and come back with the answer nobodys helpful rn and I dont know it myself really

Find 'x' in the following ​

Answers

First we have to find angle D

As it is a quadrilateral

[tex]\\ \sf\longmapsto <A+<B+<C+<D=360[/tex]

[tex]\\ \sf\longmapsto 45+50+35+<D=360[/tex]

[tex]\\ \sf\longmapsto 130+<D=360[/tex]

[tex]\\ \sf\longmapsto <D=360-130[/tex]

[tex]\\ \sf\longmapsto <D=230°[/tex]

Now

[tex]\\ \sf\longmapsto <D+x=360[/tex]

[tex]\\ \sf\longmapsto x+230=360[/tex]

[tex]\\ \sf\longmapsto x=360-230[/tex]

[tex]\\ \sf\longmapsto x=130°[/tex]

Answer:

x = 130

Step-by-step explanation:

Sum of all the angle of quadrilateral = 360°

50 + 45 + 35 + ∠ADC = 360

                130 + ∠ADC = 360

                         ∠ADC = 360 - 130

                         ∠ADC = 230

x = Reflex ∠ADC

  = 360 - 230

  = 130

Find C to two decimal places and find the measurement of angle be use your calculator

Answers

Let's solve

P=8B=5

Using Pythagorean theorem

[tex]\\ \sf\longmapsto H^2=P^2+B^2[/tex]

[tex]\\ \sf\longmapsto c^2=8^2+5^2[/tex]

[tex]\\ \sf\longmapsto c^2=64+25[/tex]

[tex]\\ \sf\longmapsto c^2=89[/tex]

[tex]\\ \sf\longmapsto c=\sqrt{89}[/tex]

[tex]\\ \sf\longmapsto c\approx 9.22[/tex]

PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER PLS GIVE ME A STEP BY STEP EXPLANATION!!

Answers

Answer:

It should be c 4,-5

hope it helps

Answer:

c. (4,-5)

Step-by-step explanation:

Point K is currently at (4,5). If reflected about x, the x-coordinate remains 4 and the y-coordinate becomes -5. Giving the answer (4,-5)

Which angle in ABC has the largest measure?

A. B. C. D. Cannot be determined

Answers

Answer:

< B has the largest angle measure.

as it is opposite to longest side of triangle.

3x - 2y = 16 and x - 2y = 4 (any method <3)​

Answers

Answer:   (x, y) = (6, 1)

This means x = 6 and y = 1

==========================================================

Explanation:

I'll use the substitution method to solve this system.

Let's solve the second equation for x

x-2y = 4

x = 4+2y

Then plug that into the first equation so we can solve for y.

3x - 2y = 16

3(4+2y) - 2y = 16 ... x replaced with 4+2y

12+6y - 2y = 16

12 + 4y = 16

4y = 16-12

4y = 4

y = 4/4

y = 1

Lastly, use this y value to find x

x = 4 + 2y

x = 4 + 2(1)

x = 6

The solution as an ordered pair is (x, y) = (6, 1)

---------------------------------

Checking the answer:

Plug those x,y coordinates into the first equation

3x - 2y = 16

3(6) - 2(1) = 16

18 - 2 = 16

16 = 16

That confirms the first equation. Repeat for the second equation

x - 2y = 4

6 - 2(1) = 4

6 - 2 = 4

4 = 4

Both equations are confirmed.

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