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
Bond [772]
3 years ago
8

An airplane is flying at an elevation of 5150 ft, directly above a straight highway. Two motorists are driving cars on the highw

ay on opposite sides of the plane, and the angle of depression to one car is 35 ̊ and to the other is 52 ̊. How far apart are the cars?

Mathematics
2 answers:
FinnZ [79.3K]3 years ago
5 0

Answer: 11378.583 feet (approx)

Step-by-step explanation:

Let from the foot of the line that shows the distance of the plane from the road the distance of first car is x feet and the distance of second car is y feet,

Thus, by the below figure,

We can write,

tan 52^{\circ}=\frac{5150}{x}

⇒ x=\frac{5150}{tan 52^{\circ}}

⇒ x = 4023.62097651

Similarly, by the below diagram,

tan 35^{\circ}=\frac{5150}{y}

⇒ y=\frac{5150}{tan 35^{\circ}}

⇒ y = 7354.96223472

Thus, the total distance between the car = x + y = 4023.62097651 + 7354.96223472= 11378.5832112≈11378.583 feet

Vladimir [108]3 years ago
3 0

Answer: 11378.58 ft


Step-by-step explanation:

1. Draw  a figure like the one attached, where A is the position of the airplane and B and C are the positions of the cars.

2. The distance between the cars is the length BC, then, you need to calculate the measure of BD and DC to add them and obtain BC.

<h2> 3. You know the opposite side and the angles of depression, then, you can calculate the distance between the cars as following:</h2>

BC=BD+DC\\BC=\frac{5150}{tan(35)}+\frac{5150}{tan(52)}\\BC=11378.58ft


You might be interested in
Find the circumference and area of a circle that has a radius of x+1
lbvjy [14]
Circumference: 2πr
Circumference: 2(3.14)(x + 1)
Circumference: 6.28(x + 1)
Circumference: 6.28(x) + 6.28(1)
Circumference: 6.28x + 6.28

Area: πr²
Area: 3.14(x + 1)²
Area: 3.14(x  +1)(x + 1)
Area: 3.14(x(x + 1) + 1(x + 1))
Area: 3.14(x(x) + x(1) + 1(x)  1(1))
Area: 3.14(x² + x + x + 1)
Area: 3.14(x² + 2x + 1)
Area: 3.14(x²) + 3.14(2x) + 3.14(1)
Area: 3.14x² + 6.28x + 3.14
6 0
3 years ago
2/5y - 4 + 7 - 9/10y with steps
Lesechka [4]

Let's simplify step-by-step.

2/ 5 y−4+7− 9 /10 y = 2 /5 y+−4+7+ −9 /10 y

Combine Like Terms:  = 2 /5 y+−4+7+ −9 /10 y

(2 /5 y+ −9 /10 y)+(−4+7) = −1 /2 y+3

Answer:  = −1 /2 y+3

Hope I could help! :)

3 0
3 years ago
Which transformations are needed to change the parent cosine function to y = 3 cosine (10 (x minus pi))?
Alekssandra [29.7K]

Answer:

See Explanation

Step-by-step explanation:

Given

New function: y = 3 \cos(10 (x -\pi))

We can assume the parent function to be:

y = \cos (x)

The new function can be represented as:

y = A*\cos((\frac{2\pi}{B})(x-c))

Where

A = Vertical stretch factor

B = Period

C = Right shift

By comparison:

y = A*\cos((\frac{2\pi}{B})(x-c)) to y = 3 \cos(10 (x -\pi))

A = 3

c = \pi

\frac{2\pi}{B} = 10

Solve for B

B = \frac{2\pi}{10}

B = \frac{\pi}{5}

Using the calculated values of A,\ B\ and\ c. This implies that, the following transformations occur on the parent function:

  • <em>Vertically stretched by </em>3<em />
  • <em>Horizontally compressed by </em>\frac{\pi}{5}<em />
  • <em>Right shifted by </em>\pi<em />
5 0
3 years ago
Read 2 more answers
I don’t get this and I need to pass it please help!!!
Novosadov [1.4K]

Answer:

Choice A x= 16, y= 9√2

Step-by-step explanation:

x= 9+7 =16

y= √9²*2= 9√2

5 0
3 years ago
Could anyone help, please?
Dmitry_Shevchenko [17]

First, find the probability of each event:

1) the probability that the spinner will land on a 7.

Since the spinner is split 4 equal sections and there is only 1 sector with 7, we can say the probability of getting a 7 is 1/4 as there is only 1 of 7 out of the total of 4 sections.

<em>and</em>

2) the probability that the spinner will land on B.

Since the spinner is split into 3 equal sections, and there is only 1 sector for B, we can say the probability of getting B is 1/3.

To find the probability of 2 events, we need to multiply the two probabilities.

1/4*1/3 = 1/12

So the answer is 1/12.

4 0
3 years ago
Other questions:
  • Y=3x+8 12x−4y=−32 ​ How many solutions does this system have?
    12·1 answer
  • What is the surface area of the cube? Drag and drop the correct surface area to match the cube. cube with edge length = 3.2 m 12
    10·1 answer
  • 30th term of 3,8,13,18
    9·1 answer
  • Which could describr the motion of an object in distance and displacement
    13·1 answer
  • Solve for x:<br><br> 30 = 14 - 4(3 - x)
    13·1 answer
  • What is the sale price of a shirt that was originally $25 but that has been marked down by 33 percent
    9·1 answer
  • I NEED THESE DONE OR I WONT GET A GOOD GRADE!!!!!
    5·1 answer
  • I'll give brainly pls help​
    8·2 answers
  • In your biology class, your final grade is based on several things: a lab score, scores on two major tests, and your score on th
    7·1 answer
  • How do you work this equation? x² + x - 30 = 0
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!