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
Ne4ueva [31]
3 years ago
12

A person is watching a boat from the top of a lighthouse. The boat is approaching the lighthouse directly. When first noticed, t

he angle of depression to the boat is 16°18'. When the boat stops, the angle of depression is 48°51'. The lighthouse is 200 feet tall. How far did the boat travel from when it was first noticed until it stopped? Round your answer to the hundredths place.
Mathematics
1 answer:
7nadin3 [17]3 years ago
4 0

To solve this problem, we can use the tan function to find for the distances covered.

tan θ = o / a

Where,

θ = angle = 90° - angle of depression

o = side opposite to the angle = distance of boat from lighthouse

a = side adjacent to the angle = height of lighthouse = 200 ft

When the angle of depression is 16°18', the initial distance from the lighthouse is:

o = 200 tan (90° - 16°18')

o = 683.95 ft

When the angle of depression is 48°51', the final distance from the lighthouse is:

o = 200 tan (90° - 48°51')

o = 174.78 ft

 

Therefore the total distance the boat travelled is:

d = 683.95 ft - 174.78 ft

<span>d = 509.17 ft</span>

You might be interested in
Dimensions of Box 2:x by 4x-1 by x^3 <br> The volume of Box 2 is given by
PIT_PIT [208]

Answer:

4x^5 – x^4

Step-by-step explanation:

i took it and was correct

6 0
2 years ago
What is the answer to 1
Burka [1]
The answer is 21. 75²=5625 72²=5184 5625-5184=441 √441=21 so 21 is your answer. I hope this helps. The formula to figure out the hypotenuse A²+B²=C² can also be used to find a leg. Since we have one leg and the hypotenuse I was able to figure this out.
8 0
3 years ago
What are the vertical asymptotes of the function f(x) = 2x + 8 / x2 + 5x + 6?
Irina18 [472]
I'm assuming the function is f(x) = (2x+8)/(x^2+5x+6). If so, make sure to use parenthesis to indicate that you're dividing all of "2x+8" over all of "x^2+5x+6" as one big fraction. Otherwise, things are ambiguous and it leads to confusion.

Side Note: x^2 means "x squared"

Factor the numerator: 2x+8 = 2(x+4)
Factor the denominator: x^2+5x+6 = (x+2)(x+3)

There are no common factors between the numerator and denominator. So there is nothing to cancel out. 

Recall that you cannot divide by zero. Something like 1/0 is undefined. 
We need to find the x values that cause the denominator to be zero.
Set the denominator equal to zero and solve for x
x^2+5x+6 = 0
(x+2)(x+3) = 0
x+2 = 0 or x+3 = 0
x = -2 or x = -3

The x values x = -2 or x = -3 will lead to the denominator being zero. This means that the vertical asymptotes are x = -2 or x = -3 as shown by the blue dashed vertical lines in the attached image.

4 0
3 years ago
432 divided by the different between 279 and 63
Debora [2.8K]
The difference (I'm assuming you meant difference) between 279 and 63 is
279 - 63 = 216
so divide 432 by 216
432 / 216 = 2
so the answer is 2
8 0
3 years ago
Find the slope of a line that passes through the
OleMash [197]

Answer:

-\frac{1}{2}

Step-by-step explanation:

To find the slope you can use the slope equation:

slope = \frac{y2 - y1}{x2 - x1}

Let's define the terms in the equation:

y2 = 5

y1 = 7

x2 = 4

x1 = 8

Now, let's put these into the equation and solve:

slope = \frac{5 - 7}{4 - 8} = -\frac{2}{4} = -\frac{1}{2}

Therefore, the slope is -1/2.

<em>I hope this helps!!</em>

<em>- Kay :)</em>

<em />

4 0
3 years ago
Other questions:
  • What can be equal to 19
    12·1 answer
  • Determine the solution set of x^2-80=0.
    15·2 answers
  • Perfume can be purchased in a 0.6-ounce bottle for $18 or in a 2-ounce bottle for $50. The difference in price per ounce is? HEL
    9·1 answer
  • What is the area of the room. Bed room #2 <br> 11-10 x10-10
    5·1 answer
  • The graph of which of the following will be parallel to the graph of 4x – 3y = –12? A.y= 4/3x -3/2 B.6x-4y=-8 C. y=3/4x+1 D.4x-
    6·2 answers
  • Use the Distributive Property to multiply 9 and 37 in your head. After 37 is in expanded form, multiply 9 by each addend. (9 × 3
    9·2 answers
  • Calculate the total cost of an item bought at a negotiated price of $17,250 with 7.7 percent sales tax and a $95 registration fe
    9·1 answer
  • Which of the tables represents a function? (5 points) Table A: Input 3 3 2 Output 1 4 3 Table B: Input 2 5 2 Output 7 6 9 Table
    15·2 answers
  • What is 142/3 simplified <br> Help please!!!
    5·2 answers
  • What is the average rate of change of f(x)=x2+x−6 between x=1 and x=3 ?
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!