An aircraft is timetabled to travel from A to B. Due to bad weather it flies from A to C then from C to B, where AC and CB make angles of 27° and 66° respectively with AB. If |AC| = 220 km, calculate |AB|.
Answers
Answer:
|AB| = 240 km
Step-by-step explanation:
Finding ∠C :
⇒ 27° + 66° + ∠C = 180°
⇒ ∠C = 180° - 93°
⇒ ∠C = 87°
Applying the Law of Sines :
⇒ sin 66° / 220 = sin 87° / AB
⇒ 0.913545458 / 220 = 0.998629535 / AB
⇒ AB = 220/0.913545458 x 0.998629535
⇒ AB = 240.819981 x 0.998629535
⇒ AB = 240.489946
⇒ |AB| = 240 km (nearest whole kilometer)
Answer:
|AB| = 240 km (nearest km)
Step-by-step explanation:
Draw a sketch with the given information (attached).
Calculate the missing angle (shown in red on the attached diagram).
Given:
∠CAB = 27°∠CBA = 66°The interior angles of a triangle sum to 180°
⇒ ∠ACB + ∠CAB + ∠CBA = 180°
⇒ ∠ACB + 27° + 66° = 180°
⇒ ∠ACB = 180° - 27° - 66°
⇒ ∠ACB = 87°
Use Sine Rule for sides to calculate |AB|:
[tex]\sf \dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}[/tex]
(where A, B and C are the angles and a, b and c are the sides opposite the angles)
[tex]\implies \sf \dfrac{|AB|}{\sin ACB}=\dfrac{|AC|}{\sin CBA}[/tex]
[tex]\implies \sf \dfrac{|AB|}{\sin (87^{\circ})}=\dfrac{220}{\sin (66^{\circ})}[/tex]
[tex]\implies \sf |AB|=\dfrac{220\:\sin (87^{\circ})}{\sin (66^{\circ})}[/tex]
[tex]\implies \sf |AB|=240.4899459...[/tex]
[tex]\implies \sf |AB|=240\:km\:(nearest\:km)[/tex]
Related Questions
Which graph represents the function f(x) = –x2 + 5? On a coordinate plane, a parabola opens down. It goes through (negative 3, negative 4), has a vertex at (0, 5), and goes through (3, negative 4). On a coordinate plane, a parabola opens up. It goes through (negative 2, 9), has a vertex at (0, 5), and goes through (2, 9). On a coordinate plane, a parabola opens down. It goes through (negative 6, negative 9), has a vertex at (negative 5, 0), and goes through (negative 2, negative 9). On a coordinate plane, a parabola opens up. It goes through (negative 8, 9), has a vertex at (negative 5, 0), and goes through (negative 2, 10).
Answers
Answer:
The graph in the attached figure
Step-by-step explanation:
we have the quadratic function
[tex]f(x)=-x^2+5[/tex]
This is a vertical parabola open downward
The vertex is a maximum
Remember that
The equation of a vertical parabola in vertex form is equal to
[tex]y=a(x-h)^2+k[/tex]
where
a is a coefficient
(h,k) is the vertex
In this problem
a=-1
(h,k)=(0,5) ----> vertex
The y-intercept is the point (0,5) ---> value of y when the value of x is equal to zero (is the same point that the vertex)
The x-intercepts are the points --->values of x when the value of y is equal to zero
using a graphing tool
The graph in the attached figure
Answer:
A on edge
Step-by-step explanation:
i took the test
Kevin walked Three-fourths of a mile in 12 minutes. Assuming he walked at a constant speed the entire time, which expression can be used to determine the distance he walked each minute?
Answers
Answer:
He walked 1/16 of an entire mile in 1 minute
Step-by-step explanation:
Jacob has 2 kilograms of flour. If his brother has one gram more than Jacob, how many grams of flour does Jacob's brother have?
Answers
4. For exercise, Francesca walks laps around a track. She walked 0.9 of a lap around the track in 5 minutes. If each lap is 440 yards, how fast did
Francesca walk?
•88 yards per minute
•360 yards per minute
•90 yards per minute
• 79.2 yards per minute
Answers
Answer:
79.2 yards per minute
Step-by-step explanation:
First you 440 times 0.9. which equals 396. Then you divide the answer by 5 to get 79.2.
What is the slope of a line that passes through the points open parentheses 5 comma 3 close parentheses and open parentheses 7 comma short dash 4 close parentheses?
Answers
Answer:
[tex]slope \: = - \frac{ 7}{2} [/tex]
Step-by-step explanation:
To find the slope of the line that passes through the points
[tex] \: {x}^{1} \: \: {y}^{1} \: \: \: \: \: \: \: \: \: \: \: \: \: \: {x}^{2} \: \: \: \: {y}^{2} \\ (5, \: \: 3) \: \: \: and \: \: (7, \: - 4)[/tex]
We have to follow the formula:
[tex] \frac{ {y}^{2} - {y}^{1} }{ {x}^{2} - {x}^{1} } \\ \\ \frac{ - 4 - 3}{7 - 5} \\ \\ slope = - \frac{ 7}{2} [/tex]
. Estimate the sum of 277 and 854 and write them in Roman numerals.
Answers
Answer:
The answer is MC = 1100. The real answer is 1131 but I have estimated the answer to the nearest hundred.
Step-by-step explanation:
I just added them up to get the real answer. The real answer is 1131 but I have estimated the answer to the nearest hundred.
The sum of 277 and 854 is 1131.
M = 1000
C = 100
X = 10
I = 1
please help will mark Brainliest!!.
Answers
Answer:
A square
Step-by-step explanation:
Its hard to mark the coordinates but its likely for it to be a square
Find the length of the indicated side.
J
3x + 17
K
8x - 8
The length of side KL is
L
Answers
Answer:
KL = 32
Step-by-step explanation:
The triangle is equilateral.
JK = KL3x + 17 = 8x - 85x = 25x = 5Finding KL :
KL = 8(5) - 8KL = 40 - 8KL = 32solve for x !
[tex]x {}^{2} - 5x + 6 = 0[/tex]
ty! :)
Answers
Step-by-step explanation:
[tex] {x}^{2} - 5x + 6 = 0\\ {x}^{2} - 3x - 2x + 6 = 0\\ x(x - 3) - 2(x - 3) = 0\\ (x - 3)(x - 2) = 0 \\ either \\ x - 3 = 0 \\ x = 3 \\ or \\ x - 2 = 0 \\ x = 2[/tex]
HELP PLEASEEE ASAPPPPPPPP
Answers
( if there wouldn’t be a global pandemic that shutdown all of the restaurants)
Mary has 6 blouses, 5 skirts and 4 belts. How many outfits can she make, consisting of a blouse, a skirt and a belt?
Answers
Answer:
120
Step-by-step explanation:
Use the counting principle.
6 × 5 × 4 = 120
Answer: 120
15
Select the correct answer.
If f(x) = (x+1)-¹ and g(x)
= x^-2, what is the domain of f(x) = g(x)?
Answers
Answer:
Step-by-step explanation:
[tex]f(x)=g(x) \implies \frac{1}{x+1}=\frac{1}{x^{2}}[/tex]
This means the denominators cannot equal to (because then the fractions would be undefined) so the domain is [tex]x \in \mathbb{R} -\{-1,0\}[/tex]
helppppppppppppppppppp
Answers
Answer:
√60
Step-by-step explanation:
6² = 36 ⇒ √36 = 6
8² = 64 ⇒ √64 = 8
⇒ 6 < x < 8
⇒ √36 < x < √64
Therefore, we need the square root of a number between 36 and 64.
From the given options, √60 is the only available option as:
√36 < √60 < √64
⇒ 6 < √60 < 8
Therefore, √60 is greater than 6 and less than 8.
√60
Because
Square of rest two numbers
6²=368²=64As
60 lies in between 36 and 64
So
√60 lies in between 6 and 8.
Teresa is maintaining a camp fire. She can
keep the fire burning for 4 hours with 6 logs.
She wants to know how many logs (y) she
needs to keep the fire burning for 18 hours.
She assumes all logs are the same.
How many logs does Teresa need to
maintain the fire for 18 hours?
Answers
Answer:
27
Step-by-step explanation:
she needs 24 logs to keep the fire for 16 hours(4×6). And for next 2 hours she's gonna need 3. altogether it's 27.
Contagious diseases can spread quickly. Suppose 3 people are ill during the first week of an epidemic, and each person who is ill spreads the disease to five people by the end of the next week. By the end of the 8th week of the epidemic, how many people have become ill?
Answers
Answer:
1875
Step-by-step explanation:
3x5 = 15
15x 5 = 75
75x 5 = 375
375 x 5 = 1875
1875 because at the end of the next week, which basically turns 8 weeks into 4, and the number of contaminants multiply by 5 each other week.
A box contains orange balls and green balls. The number of green balls is ten more than four times the number of orange balls. If there are 110 balls altogether, then how many green balls and how many orange balls are there in the box?
Answers
Answer:
there are 50 orange balls
Step-by-step explanation:
let green balls be x
orange balls be y
green balls = orange balls + 10
x = y+10
orange balls + green balls = 110
x + y = 10
y + 10 + y = 110
2y + 10 = 110
2y = 110 -10
2y = 100
y = 50
thus there 50 orange balls
To multiply 64 • 8.32, use the logarithmic equation:
1) log 72.32
2) log 64 + log 8.32
3) antilog 64 + antilog 8.32
4) (log 64)(log 8.32)
Answers
To multiply 64 × 8.32 use the logarithm equation 2)㏒64 + ㏒8.32
To answer the question, we need to know what logarithm of a number is
What is the logarithm of a number?The logarithm of a number x is the power to base 10 of that number.
So, logarithm of x to base 10 is written as ㏒x.
Since we want to multiply 64 × 83.2, we convert this to logarithmic equation using the addition rule of logarithm.
Addition rule of logarithm㏒ab = ㏒a + ㏒b
So, 64 × 8.32 to logarithm is ㏒(64 × 8.32) = ㏒64 + ㏒8.32
So, to multiply 64 × 8.32 use the logarithm equation 2)㏒64 + ㏒8.32
Learn more about logarithm here:
https://brainly.com/question/26788007
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PLEASE HELP WILL MARK BRSINLIEST!!!!!
Answers
Answer:
AC=18
Step-by-step explanation:
Let's look at the smaller triangle first. Side AB is 2.5, side BC is 3.5 and side AC is 4.5. Now, looking at the larger triangle, we see that side AB is 10, side BC is 14 and side AC is unknown.
So, how do we find side AC?
First, let's take a look at the other sides available to us—how about AB? On the smaller triangle, AB=2.5, and on the larger triangle AB=10. So, what's their relation?
Well, let's first divide the two by each other: 10/2.5, of which gets us 4. Now, this in itself gives us answer, but let's just double check to be sure. So, taking side BC on the smaller triangle, 3.5, and on the larger triangle, 14, we then divide the two again. 14/3.5 and- look at that! We get 4 again again.
This tells us that 4 is then our multiplier, so we can write the equation as follows: 4.5 (of which we get from the smaller triangle) *4=?. So, with the equation 4.5*4, we get 18 as our answer for ?, or simply the unknown side "a".
Vera needs repairs on her car. The mechanic’s estimate says that he will provide 7.3 hours of labor. His rate is $55 per hour. The total cost of the labor will be
Answers
Explanation: 55$ • 7.3 = $401.5
Hope this helps! Please give me feedback based on my answer to you (stars, hearts, brainliest) thanks so much :)
Ella conducted a survey to find out the amount of time high schoolers spend surfing the Internet. From the data collected, the range of time spent was 1 hour. What does this range say about the data?
All the students surveyed spend exactly 1 hour surfing the Internet.
All the students surveyed spend an average of 1 hour surfing the Internet.
The difference between the greatest amount of time and the least amount of time spent surfing the Internet is 1 hour.
The quotient between the greatest amount of time and the least amount of time spent surfing the Internet is 1 hour.
Answers
The statement third “the difference between the greatest amount of time and the least amount of time spent surfing the Internet is 1 hour” is correct.
What is range?It is defined as the difference between the maximum value in the data set to the minimum value in the data set.
As we know, the difference between the greatest and lowest values, called the range.
According to this response, the range is 1 hour, which is the difference between the most and least amount of time spent surfing the Internet. This is based on the term “Range.”
Thus, the statement third “the difference between the greatest amount of time and the least amount of time spent surfing the Internet is 1 hour” is correct.
Learn more about the range here:
https://brainly.com/question/17553524
#SPJ1
Answer:
The difference between the greatest amount of time and the least amount of time spent surfing the Internet is 1 hour!
Step-by-step explanation:
please help will mark Brainliest!!.
Answers
Explanation: 2pi r
2 • 3.14 • 2
Hello please help me………….thank you
Answers
Answer:
1. False —> that’s how you find the perimeter.
2. False —> area is measured in square units.
3. False —> you can only use a multiplication.
4. True —> (2x6) + (2x8) = 28 inches.
5. False —> 5x5 = 25 square meters.
—-
Have a nice day!!
Answer:
Step-by-step explanation:
1 False. The suggestion given is for Perimeter, not area.
2 False. The perimeter is given in units not square units. For example, the Perimeter of square with one side of 7 in is 4 * 7 inches is 28 inches
3 False. You can only use multiplication equations to find a rectangle's area (or at least it is the easiest way to do it.) Higher math courses find areas by using multiplication and addition, but I'm pretty sure you are not in a higher math course.
4.True
5 False. The area of a square is 5 * 5 = 25. Not 4*5 = 20
Step 1: –10 + 8x < 6x – 4
Step 2: –10 < –2x – 4
Step 3: –6 < –2x
Step 4: ________
What is the final step in solving the inequality –2(5 – 4x) < 6x – 4?
x < –3
x > –3
x < 3
x > 3
Answers
x > 3
Step-by-step explanation:
The final step in solving the inequality –2(5 – 4x) < 6x – 4 is
-6/-2 < x = 3 < x
Question 16
The triangular prism below represents the shape of Sylvia's tent.
Sylvia's Tent
6 feet
6 feet
10 feet
8.5 feet
What is the volume of the tent in cubic feet?
C 255
D 360
A 180
B 241
1 point
Answers
Answer:
180^3'
Step-by-step explanation:
6x6=36.
36x10=360.
360 divided by 2= 180.
:}
Convert: 8 tons = _____ pounds
4 pounds
80 pounds
8,000 pounds
16,000 pounds
Answers
8 tons = 2000x8 = 16000 pounds
answer : 16000 pounds
Answer:
16,000 pounds hope this helps!
What happens with rotational symmetry?
Answers
Answer:
The shape of an object looks the same when an object is rotated on it's own axis
What is the solution?
Answers
Answer:
1200c^3
Step-by-step explanation:
cut the shape it to half with a square and a prism and calculate them separately then add the volume!
Hope this helps! ;-)
Need help for this please
Answers
Step-by-step explanation:
what is the problem ?
we only need to use the formula that can be found easily on the internet.
the area of a circle is
pi×r²
r being the radius (half of the diameter). in our case :
14/2 = 7 m
and we shall use 22/7 as approximation for pi.
so, we get as circle area
22/7 × 7² = 22 × 7 = 154 m²
Determine the distance between the points plotted on the graph. Round to the nearest tenth, if necessary.
Answers
Answer:
d= 4[tex]\sqrt{2}[/tex] or 5.66
Step-by-step explanation:
(-2,7) and (2,3)
d = [tex]\sqrt{(x2-x1)^{2} + (y2-y1)^{2} }[/tex]
d= [tex]\sqrt{(2-(-2))^{2} + (3-7)^{2} }[/tex]
d = [tex]\sqrt{16 + 16}[/tex]
d= 4[tex]\sqrt{2}[/tex] or 5.66
Harry invests $1000 in an investment account that earns 6% interest, compounded annually. How much money will he have in the account after 30 years?
Answers
the answer to that question is 1800