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
vladimir1956 [14]
2 years ago
14

From the top of a lighthouse 240 feet high, the angle of depression to a boat out on the water is 23 degrees. Find the distance

from the boat to the bottom of
the lighthouse. Round your answer to the nearest foot.
Mathematics
1 answer:
g100num [7]2 years ago
3 0

Answer:   565 feet

This value is approximate.

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

Explanation:

Imagine you are at the top of the lighthouse, and look straight horizontally outward. Then imagine looking down 23 degrees to spot the boat. This forms the angle of depression.

The adjacent angle complementary to this is 90-23 = 67 degrees. This is the interior angle of the triangle needed, and this angle is at the top of the triangle.

tan(angle) = opposite/adjacent

tan(67) = x/240

x = 240*tan(67)

x = 565.4045677977 approximately

x = 565 feet

The diagram is below.

You might be interested in
4) This results when you flip the numerator and denominator of a fraction.
Semenov [28]

Answer:

To divide one fraction by another one, flip numerator and denominator of the second one, and then multiply the two fractions. The flipped-over fraction is called the multiplicative inverse or reciprocal.

Step-by-step explanation:

I got this from google.

3 0
3 years ago
Nine workers are hired to weed a field by
Dmitriy789 [7]

Answer:

144

Step-by-step explanation:

12x12=144

4 0
3 years ago
If <img src="https://tex.z-dn.net/?f=%20300cm%5E%7B2%7D%20" id="TexFormula1" title=" 300cm^{2} " alt=" 300cm^{2} " align="absmid
Artist 52 [7]
Check the picture below.  Recall, is an open-top box, so, the top is not part of the surface area, of the 300 cm².  Also, recall, the base is a square, thus, length = width = x.

\bf \textit{volume of a rectangular prism}\\\\&#10;V=lwh\quad &#10;\begin{cases}&#10;l = length\\&#10;w=width\\&#10;h=height\\&#10;-----\\&#10;w=l=x&#10;\end{cases}\implies V=xxh\implies \boxed{V=x^2h}\\\\&#10;-------------------------------\\\\&#10;\textit{surface area}\\\\&#10;S=4xh+x^2\implies 300=4xh+x^2\implies \cfrac{300-x^2}{4x}=h&#10;\\\\\\&#10;\boxed{\cfrac{75}{x}-\cfrac{x}{4}=h}\\\\&#10;-------------------------------\\\\&#10;V=x^2\left( \cfrac{75}{x}-\cfrac{x}{4} \right)\implies V(x)=75x-\cfrac{1}{4}x^3

so.. that'd be the V(x) for such box, now, where is the maximum point at?

\bf V(x)=75x-\cfrac{1}{4}x^3\implies \cfrac{dV}{dx}=75-\cfrac{3}{4}x^2\implies 0=75-\cfrac{3}{4}x^2&#10;\\\\\\&#10;\cfrac{3}{4}x^2=75\implies 3x^2=300\implies x^2=\cfrac{300}{3}\implies x^2=100&#10;\\\\\\&#10;x=\pm10\impliedby \textit{is a length unit, so we can dismiss -10}\qquad \boxed{x=10}

now, let's check if it's a maximum point at 10, by doing a first-derivative test on it.  Check the second picture below.

so, the volume will then be at   \bf V(10)=75(10)-\cfrac{1}{4}(10)^3\implies V(10)=500 \ cm^3

6 0
3 years ago
Anya’s team won 5 out of every 7 games this season.
Colt1911 [192]

Answer:

They won 15 games

Step-by-step explanation:

I am smart

Mark ME BRAINLIEST PLEASE

3 0
3 years ago
Read 2 more answers
Help will give the branniest
Naily [24]

The answer is C... Hope it helps

4 0
3 years ago
Other questions:
  • Can someone help me plz<br> (-5x^4y^2)^3
    15·1 answer
  • You sell T shirts for a fundraiser. It cost $122 to have the shirt made . You make $98 in sales . What is your profit ?
    14·1 answer
  • Which term describes the slope of the graph of song 1 between minute 3 and minute 4
    7·2 answers
  • Write all of the digita that can rwplace each 735&lt;7 ■ 4&lt;761
    6·1 answer
  • Solve please 4x^2+2x-10=0
    5·2 answers
  • A financial advisor puts 1/10 of all income into a savings account and puts the rest into a checking account. Which statement is
    9·1 answer
  • 5 customers approach your truck each with a coupon for 2 dollars. The total amount of money they will spend can be represented b
    6·1 answer
  • Two points, (-2,4) and (2,4), are plotted on a coordinate grid.
    15·1 answer
  • If (-1,0) belong to the function f where f(x) =M X +2, then M= <br><br>Pls answer ​
    7·1 answer
  • What is the slope of this line?
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!