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
Citrus2011 [14]
1 year ago
12

an airplane flying at an elevation of 3,500 ft., directly above a straight highway. two motorists are driving cars on the highwa

y on opposite sides of the plane. the angle of depression to one car is 31 degrees and to the other is 53 degrees. how far apart are the cars?
Mathematics
1 answer:
rosijanka [135]1 year ago
6 0

The first and second cars are 7724 feet apart from each other.

The angle of depression is the angle we have to move your eyes downwards to look at the car from the plane. Let's start with the first car, with the 31° angle of depression. Draw an upside-down right triangle with vertices at the plane, the car, and the point 3500 feet in the air above the car (level with the plane). The vertex at the plane is 31° and the right angle is the vertex in the air above the car. The length of the leg from the car to the point in the air above the car is 3500 feet. We like to find the length of the leg from the plane to the point in the air above the car. Since the two sides involved are the legs of the triangle, use tangent:

     tan = opposite/ adjacent

⇒  tan(31°) = 3500/x

⇒ 0.60086 = 3500/x

⇒ 0.67 x = 3500            [ rounding up 0.60086 = 0.67]

⇒ x = 5223.88

That means the first car is 5223.88 feet from the point on the highway below the plane.

We can do something similar with the second car, which has an angle of depression of 53° from the plane. Again, the leg from the car to the point in the air above the car (level with the plane) is 3500 feet, the right angle is at the vertex at the point in the air above the car, and the 53° angle is at the vertex at the plane. We are looking for the length of the other leg, which runs from the plane to the point in the air above the car. Use tangent:

    tan(53°) = 3500/x

⇒ 1.327 = 3500/x

⇒ 1.4x = 3500            [ rounding 1.327 = 1.4]

⇒ x = 3500/1.4
⇒ x = 2500

That means the second car is 2500 feet from the point on the highway below the plane.

Add the two distances together to get the total distance from car to car:

5223.88 + 2500.00 = 7723.88

So, rounded to the nearest foot, the cars are 7724 feet apart.

Learn more about Vertex:

brainly.com/question/29030495

#SPJ4

You might be interested in
Write each percent as a fraction and as a decimal to the nearest hundredth.
Nataly [62]
Each as a fraction 42/100 35/100 18/100 100/100
8 0
3 years ago
What is the least common denominator of<br> 1/3 and 5/9
crimeas [40]

Answer:

<h2>LCD = 9</h2>

Equivalent Fractions with the LCD

1/3 = 3/9

5/9 = 5/9

Solution:

Rewriting input as fractions if necessary:

1/3, 5/9

For the denominators (3, 9) the least common multiple (LCM) is 9.

LCM(3, 9)

Therefore, the least common denominator (LCD) is 9.

Calculations to rewrite the original inputs as equivalent fractions with the LCD:

1/3 = 1/3 × 3/3 = 3/9

5/9 = 5/9 × 1/1 = 5/9

4 0
3 years ago
The sum of two integers is 60 and their difference is 8 find the integers
slega [8]

Answer:

Step-by-step explanation:

x+y = 60

x-y = 8

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

2x = 68

x = 34

y = 60-x = 26

4 0
2 years ago
HURRY PLSSS
vodka [1.7K]

Answer:

C)

Step-by-step explanation:

the answer is c because you multiply 4 and 2 and get 8 and multiply 8 by 8 and get 64 then you use 4 again and multiply 64 by 4 so you get 256 and round that 254

6 0
3 years ago
Read 2 more answers
Divide 33 photos into two groups so the ratio it 4 to 7
katrin2010 [14]
4 to 7......add them = 11

4/11 * 33 = 132/11 = 12
7/11 * 33 = 231/11 = 21
8 0
3 years ago
Read 2 more answers
Other questions:
  • 34 days to 2 weeks the ratio is
    5·1 answer
  • Write each decimal as a fraction or mixed numbest form. -7.08
    7·1 answer
  • What is 18049 divided by 14
    10·1 answer
  • Please help ASAP :)))))
    13·1 answer
  • Can someone help me with this
    10·2 answers
  • What is the answer here and explain why.
    6·2 answers
  • Im giving brainliest<br> FREE
    15·1 answer
  • Binary add<br>i) 10101 + 1001​
    13·2 answers
  • the instructor has save $3500 and rents an apartment for $275 monthly. he believes the point 6, 1850 would be on the equation of
    7·1 answer
  • 26 rooms on 2 floors = ____ rooms on 4 floors
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!