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
Alisiya [41]
3 years ago
6

6. Two observers, 7220 feet apart, observe a balloonist flying overhead between them. Their measures of the

Mathematics
1 answer:
MaRussiya [10]3 years ago
6 0

Answer:

The ballonist is at a height of 3579.91 ft above the ground at 3:30pm.

Step-by-step explanation:

Let's call:

h the height of the ballonist above the ground,

a the distance between the two observers,

a_1 the horizontal distance between the first observer and the ballonist

a_2 the horizontal distance between the second observer and the ballonist

\alpha _1 and \alpha _2 the angles of elevation meassured by each observer

S the area of the triangle formed with the observers and the ballonist

So, the area of a triangle is the length of its base times its height.

S=a*h (equation 1)

but we can divide the triangle in two right triangles using the height line. So the total area will be equal to the addition of each individual area.

S=S_1+S_2 (equation 2)

S_1=a_1*h

But we can write S_1 in terms of \alpha _1, like this:

\tan(\alpha _1)=\frac{h}{a_1} \\a_1=\frac{h}{\tan(\alpha _1)} \\S_1=\frac{h^{2} }{\tan(\alpha _1)}

And for S_2 will be the same:

S_2=\frac{h^{2} }{\tan(\alpha _2)}

Replacing in the equation 2:

S=\frac{h^{2} }{\tan(\alpha _1)}+\frac{h^{2} }{\tan(\alpha _2)}\\S=h^{2}*(\frac{1 }{\tan(\alpha _1)}+\frac{1}{\tan(\alpha _2)})

And replacing in the equation 1:

h^{2}*(\frac{1 }{\tan(\alpha _1)}+\frac{1}{\tan(\alpha _2)})=a*h\\h=\frac{a}{(\frac{1 }{\tan(\alpha _1)}+\frac{1}{\tan(\alpha _2)})}

So, we can replace all the known data in the last equation:

h=\frac{a}{(\frac{1 }{\tan(\alpha _1)}+\frac{1}{\tan(\alpha _2)})}\\h=\frac{7220 ft}{(\frac{1 }{\tan(35.6)}+\frac{1}{\tan(58.2)})}\\h=3579,91 ft

Then, the ballonist is at a height of 3579.91 ft above the ground at 3:30pm.

You might be interested in
Find the values of x and y - i will give brainliest if right
kherson [118]

Answer:

itd x=68 and y=5 I apolgize if its wrong

4 0
2 years ago
50 points! Someone actually help instead of putting random answers! Random answers will be reported
In-s [12.5K]

<em>If</em><em> </em><em>you</em><em> </em><em>only</em><em> </em><em>want</em><em> </em><em>to</em><em> </em><em>see</em><em> </em><em>the</em><em> </em><em>way</em><em> </em><em>i do</em><em> </em><em>it</em><em> </em><em>to</em><em> </em><em>get</em><em> </em><em>the</em><em> </em><em>answer</em><em> </em><em>without</em><em> </em><em>seeing</em><em> </em><em>my</em><em> </em><em>explanation</em><em> </em><em>ignore</em><em> </em><em>sentences</em><em> </em><em>with</em><em> </em><em>symbol</em><em> </em><em>'</em><em>#</em><em>'</em>

<h2>Answer</h2>

•Pic on the left

x = 8.36

y = 140.18°

• Pic on the right

x = 110°

<h2>Way to do</h2>

• This one for the pic on the left

#Since the total degree of a triangle is 180° and one of the side known 90° (L) so the rest must be 90° (180° - 90° = 90°)

#known that the other side of triangle degree is (5x - 2)° and 6x° so... u can find the x! :D

90 = (5x - 2) + 6x

90 = 11x - 2

90 + 2 = 11x

92 = 11x

x = 92 : 11

x = 8.36 (2 decimal places)

#Now you know the x, you can now find the degree

#degree of (5x - 2)

5x - 2 =

5(8.36) - 2 =

41.81 - 2 = 39.81

#Since the y° is in the other side of the line of degre 39.81°, you can find it by minus it with 180° (straight line with no degree is 180°)

180° - 39.81° = 140.18

•This one for the pic on the right

#Lol this one is easy. I already told you before that the straight line degree is 180° and you can find one of the side if you know one of the degree side, so you can find it.

# Also as i said before, total triangle degree is 360°

#Find the degree of the other side of x° (only can find the degree of other side x because its inside the triangle)

Degree = 180° - 80° - 30° = 70°

#Now you can get x

x = 180° - 70° = 110°

<h2>For moderators that see this</h2>

#Moderators please don't be mean, dont delete my answers just for approval from your senior or just to get the biggest moderation daily rank. This answer is long, how can you just instanly delete it? :(

7 0
3 years ago
Read 2 more answers
The table shows one point from the given graph. How could you find more ordered pairs to create a graph and table of equivalent
11Alexandr11 [23.1K]

Answer:

A,B,D

Step-by-step explanation:

JUST TOOK THE QUIZ

3 0
3 years ago
Read 2 more answers
I need help with this graph! I need to solve this equation to understand where to graph the points, I really need help on this t
kvv77 [185]

Answer:2

Step-by-step explanation:

3 0
2 years ago
Read 2 more answers
Evaluate 35/a when a=7.
slega [8]

Answer:

5

Step-by-step explanation:

5 0
3 years ago
Other questions:
  • Use the quadratic function to predict f(x) if x equals 2. f(x) = −3x2 + 180x − 285
    6·2 answers
  • The weight of water is 62 1/2 lb per cubic foot water that weighs 300 lb will fill how many cubic feet
    12·1 answer
  • Click on the value for p that makes this<br> inequality true.<br><br><br><br> Pls I need this
    10·2 answers
  • Let M={-2,-1,0,2,} in universe U={-3,-2,-1,0,1,2,3,4} Which wet is the complement of set M?
    11·1 answer
  • 16.437 rounded to the nearest tenth is 164.
    13·1 answer
  • Caleb types 100 words in 5 minutes. What is the unit rate? 100 words to 5 minutes 5 minutes per 100 words 20 words per minute 1
    5·2 answers
  • A surveyor measures from a point on the ground level that is 40 feet away from the building. the surveyor noted that the angle f
    12·1 answer
  • 15
    12·1 answer
  • I need help on this exam for math correct answers please
    14·1 answer
  • You invested $27,200 and started a business selling vases. Supplies cost $11 per
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!