A buoy is floating in the sea and can be seen from the top of a vertical cliff. A boat is travelling from the base

of the cliff directly towards the buoy. The top of the cliff is 142 m above sea level. The angle of depression

from the top of the cliff to the buoy is 40 degrees.

Answers

Answer 1

Answer:

169.23m

Step-by-step explanation:.

Let's calculate the base of the cliff. Using SOH CAH TOA identity

Height (opposite) = 142n

Angle of depression = 40°

Required

Base of the cliff

Tan theta = opposite/adjacent

Tan 40 = 142/x

x = 142/tan40

x = 142/0.8391

x = 169.23m

Hence the base of the cliff is 169.23m long


Related Questions

im being timed
which number line represents the solution set for the inequality?​

Answers

Answer:

The solution is:

[tex]-\frac{1}{2}x\ge \:4\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x\le \:-8\:\\ \:\mathrm{Interval\:Notation:}&\:(-\infty \:,\:-8]\end{bmatrix}[/tex]

The number line graph of the solution is also attached below.

From the graph, it is clear that the 2nd number line represents the solution set for the inequality.

Step-by-step explanation:

Given the inequality

[tex]-\frac{1}{2}x\ge 4[/tex]

Let us solve the inequality

[tex]-\frac{1}{2}x\ge 4[/tex]

Multiply both sides by -1 (reverse the inequality)

[tex]\left(-\frac{1}{2}x\right)\left(-1\right)\le \:4\left(-1\right)[/tex]

Simplify

[tex]\frac{1}{2}x\le \:-4[/tex]

Multiply both sides by 2

[tex]2\cdot \frac{1}{2}x\le \:2\left(-4\right)[/tex]

Simplify

[tex]x\le \:-8[/tex]

Thus, the solution is:

[tex]-\frac{1}{2}x\ge \:4\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x\le \:-8\:\\ \:\mathrm{Interval\:Notation:}&\:(-\infty \:,\:-8]\end{bmatrix}[/tex]

The number line graph of the solution is also attached below.

From the graph, it is clear that the 2nd number line represents the solution set for the inequality.

Erin buys 4 packs of potatoes costing £2 each, 2 packs of carrots for £3 per pack, and 5 turnips costing 70p each.
If she pays with a £20 note, how much change would she get in pounds, £?​

Answers

She would get £2.50

4 times 2 is 8
2 times 3 is 6
0.7 times 5 is 3.5
Add them together
Minus it from 20
It equals £2.50


¿Si tienes un cilindro de 12 m de diámetro y un prisma de base cuadrada de 12m de lado cual tiene mayor volumen si la altura es la misma?

Answers

12+12=24 give me brainlyest

You go to the restaurant and order $137.00 worth of food. You decided to tip the waiter 18%. You also have to pay tax of 6.5% on the original bill. What is the final cost of the meal?

Answers

Answer: $1, 615

Step-by-step explanation:



HELP FAST PLS
What is the volume of this container?
4 ft²
2 ft
2 ft²
I ft
4 ft?
I ft
2 ft²

Answers

Answer:

2ft3

Step-by-step explanation:

V=lengthxwidthxheight

1ftx1ftx2ft

V=2

2 ft 3 is the correct answer

solve the inequality 7x+5>2x+35

Answers

Answer:

x>7

Step-by-step explanation:

7x +5 > 2x +35

-2x -5  -2x

5x>35

x>7

help me plzzzzzzzzzzz this is for a grade dont know how to do it

Answers

Answer:

B

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

V = pi r^2 h

isolate h by moving pi & r^2 to the other side.  

Move with opposite operation from multiplying which is dividing, so

h = V / (pi r^2)

whats 14/3 simplified to

Answers

Answer:

4.666667

Step-by-step explanation:

Answer:

You cant simply it.

Step-by-step explanation:

14/3 is the simplest version of 14/3. If you were looking for decimal form its 4.666667

What is the slope of the line that passes through the points (3,8) and (8,13) write the answer in simplest form

Answers

Answer: y=5

X=5

5/5 or 1

Step-by-step explanation:

What is the horizontal asymptote

Answers

Answer:

i think the green line would be the horizontal asymptote cause its like horizontal amd it goes across the graph.

Step-by-step explanation:

Eşit sayıda yolcu taşıyan 3 otobüste toplam 93 yolcu vardır. Otobülerden birer
tane yolcu iniyor otobüste kaç yolcu kalır?​

Answers

Her otobüste esit dediğinden 93 ÷3den 31 yolcu vardır

Her otobüsten eşit sayıda yolcu indiğinde 31-1 den 30 yolcu kalır

Her otobüste 30 yolcu kaldığından ve 3 otobus olduğundan 30 ×3 den 90 yolcu kalir

It’s hard:(( pls help

Answers

Answer:

what the question i can't see that

Step-by-step explanation:

i think it’s four because the degree is 80 and the one side has a degree of 80 and the length is four

3. Write each number as a product of its prime factors:
a) 48
b) 441
c) 420
d) 1617
de 10​

Answers

Answer:

Step-by-step explanation:

I need help in this question

Answers

Answer:

128

Step-by-step explanation:

Answer:

128 correct me if Im wrong

Step-by-step explanation:

To write it out you would write 2 x 2 x 2 x 2 x 2 x 2 x 2=  and that equals 128

A. Suppose an angle measure is 55 degrees. What is the measure of its complementary angle? Draw the angle and label both measures.
B. Suppose an angle measure is 110 degrees. What is the measure of its supplementary angle? Draw the angle and label both measurements.

Answers

Answer:

A: 45 degrees

B: 70 degrees

Step-by-step explanation:

A: Complimentary angles add up to 90      90-55=45

B: Supplementary angles add up to 180      180-110=70

When might term insurance be a better option than whole life insurance???
HURRY PLS

Answers

Answer:

Term life insurance plans are much more affordable than whole life insurance. This is because the term life policy has no cash value until you or your spouse passes away. In the simplest of terms, it's not worth anything unless one of you were to die during the course of the term. Then that's when you receive money..

Step-by-step explanation:

(G0OGLED THE ANSWER)

Term insurance can be a better product if your time horizon is 10 years or less. Term insurance is better than whole life insurance especially at younger ages. Also term insurance works best because it is a low cost and low commitment program.

Janice has 400g of sugar and 2 kg of flour. She says that the ratio of sugar to flour simplifies to 200:1. Explain why she is incorrect and give the correct answer.

Answers

Answer:

she is incorrect because it is 1:5

Step-by-step explanation:

1000g in a kg

0.4kg:2kg

1:5

which method would i use to solve ax^2+c=d? justify your answer.

Answers

9514 1404 393

Answer:

  x = ±√((d -c)/a)

Step-by-step explanation:

The usual "solve for ..." approach works fine in this case.

  ax^2 +c = d

  ax^2 = d - c . . . . . subtract c

  x^2 = (d -c)/a . . . . divide by a

  x = ±√((d -c)/a) . . . take the square root

_____

When there are numbers, a graphical solution could work. It depends on whether an exact or approximate solution is required.

_____

Comment on "solve for ..."

When solving an equation for a specific variable, it is worthwhile to consider the Order of Operations. Look at what has been done to the variable, then undo those operations in reverse order. Here, the variable has been squared, the product multiplied by 'a', that product added to c. So, the "undo" consists of subtracting 'c', dividing by 'a', and taking the square root.

I NEED SERIOUS HELP I AM HAVING MATH EXAM SOON

PLEASEEEEEEEEEE HELP ME IM PREPARING WITH THE PPTS MY TEACHERS HAVE GAVE ME BUT THEY GAVE NO ANSWER AND IM NOT ABLE TO SOLVE THIS(I asked this before itself but never got an answer so with extra details I'm hoping I will get some answers) its my 4th time my first try no one answered so I put another one then I forgot to attach the photo and third time a person wasted your chances so this my 4th time BUT PLEASE HELP MEHHH

Answers

Answer:

Vertices are basically the point where 2 sides meet. In this shape the vertices are:

A, B and C

The sides are;

AB. BC, and CA

The angles are all 60°, this is because it is an equilateral triangle (all the sides seems to be equal)

HELP are all three of these are either
One Unique Triangles
Multiple Triangles
No triangles

Answers

the first is no triangles, second Multiple Triangles, third Multiple Triangles

Step-by-step explanation:


What is the inscribed angle and the circumscribed angle​

Answers

the inscribed angle is the one on the inside of the circle and the circumscribed angle is the right angle on the outside of the circle :)

Which of the following statements are ALWAYS true?


A rhombus is a kite.

A rhombus is a parallelogram.

A rhombus is a square.

A rhombus is a quadrilateral.

Answers

Answer:

a rhombus is a quadrilateral

Answer:

A rhombus is a quadrilateral .

Step-by-step explanation:

A rhombus is a parallelogram with four congruent sides

So b) and d)

--8x + 10y = 16
-4x - 5y = 13

Answers

Step-by-step explanation:

please refer to the attachment

Substitution Method

{ -8x+10y=16
{ 4x-5y=13

{ -8x+10y=16
{ x=13/4+5/4y

-8(13/4+5/4y)+10y=16

No solution

——

Elimination Method

{ -8x+10y=16
{ 4x-5y=13

{ -4x+5y=8
{ 4x-5y=13

0=21

Still, there is no solution.

A student is asked to write a report about the population growth of two countries A and B. The population of these two countries over the past five years is shown in the table below, The population of both countries is expected to continue to grow at the same rate. Which if the following statements can the students use in their report to accurately describe the population of Country A? Select two that apply. it is decreasing each year at a constant rate., It is increasing linearly., It will always be less than the population of Country B., It is increasing exponentially., It will eventually exceed the population of Country B lo

Answers

Answer: The answer is It will eventually exceed the population of Country B. The other answer is It is increasing exponentially

Step-by-step explanation:

The correct answers would be statements (C) and (D) for the given table.

What is an exponential function?

An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.

The population of these two countries for the last five years is displayed in the given table. Both countries' populations are predicted to continue growing at the same rate.

The following statements can the students use in their report to accurately describe the population of Country A, as:

It will eventually exceed the population of Country B.

It is increasing exponentially.

Hence, the correct answers would be statements (C) and (D).

Learn more about exponential function here:

brainly.com/question/11487261

#SPJ6

Need help po. Salamat

Answers

Answer:

1. y ≥ 100

2. y ≤ 300

3. y ≥ 20000

4. 2y ≥ 80

5. 2y ≤ 90

Step-by-step explanation:

Let y be the variable.

1. The discount is not less than 100.

If the discount (i.e y) is not less than 100, it means it is either 100 or greater than 100.

This can be written as:

y ≥ 100

2. The cost of the book is at most 300.

This implies that the cost of the book (i.e y) is either 300 or lesser.

This can be written as:

y ≤ 300

3. His monthly income is at least 20000. This simply means that his monthly income (i.e y) is 20000 or greater than 20000.

This can be written as:

y ≥ 20000

4. Twice the number is at least 80.

Let the number be y.

Twice the number y can be written as:

2y

But twice the number is at least 80.

This means that twice the number is 80 or greater than 80. This can be written as:

2y ≥ 80

5. Twice the measure of the acute angle is not more than 90 degree.

Let the angle be y.

Twice the angle can be written as:

2y

But twice the measure of the angle is not more than 90 degree. This implies that twice the angle is 90 or lesser than 90. This can be written as:

2y ≤ 90

work out the y-4 when y=10​

Answers

10-4= 6 so the answer is 6
10-4=6 is your answer

I NEED HELP LIKE NOW!!!! PLEASE!

Rewrite y = sqrt16x+80 - 4 to make it easy to graph using a translation. Describe the graph.

Thank you!

Answers

Answer:

Wat w Polsce i w sumie to nic innego niż

For the circle x^2 + y^2 = 100, a) State the radius at 6,8

Answers

Answer:

add multiply divide or subtract make sure to use Pemdas then and you should have your answer

Step-by-step explanation:

Answer:

r = 10

Step-by-step explanation:

The equation of a circle centred at the origin is

x² + y² = r² ( r is the radius )

x² + y² = 100 ← is a circle centred at the origin with

r² = 100 ( take the square root of both sides )

r = [tex]\sqrt{100}[/tex] = 10

174 x 206 x 532 x 174

Answers

Answer:

3318007392

Step-by-step explanation:

174 x 206 x 532 x 174 = 3318007392

sorry is if this answer wrong:)

Step-by-step explanation:

174×206×532×174=

= 3,138,007,392

I hope this helps

At the end of summer sale, an air conditioner that sold for $310 was discounted for 21%. What was the sale price?

Answers

Answer:

The sale price was $244.9.

Step-by-step explanation:

With the information provided, you can calculate the sale price by finding the 21% of the sale price and then, subtracting that amount from the sale price:

$310*21%=$65.1

$310-$65.1=$244.9

According to this, the answer is that the sale price was $244.9.

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