a crew is setting up a zip line between two towers with support wires as shown in the figure (not to scale). they only know the heights of the towers and the angles that two of the supports make with the ground. what is the length of the zip line?
Answers
Answer:
length of the zip line = 121. 63 ft
Step-by-step explanation:
The length of the zip line AB forms a triangle ABC. To find the length AB we need to know the length of 2 sides of the triangle an angle.
Triangle ADC
We need to find the hypotenuse side AC using the SOHCAHTOA principle.
Therefore,
sin 41° = opposite/hypotenuse
opposite = 65 ft
sin 41° = 65/AC
cross multiply
0.65605902899 AC = 65
divide both sides by 0.65605902899
AC = 65/0.65605902899
AC = 99.0764506359 ft
AC ≈ 99.08 ft
Triangle BCE
We are looking for side BC. The triangle BCE is also a right angle triangle so we use the same methodology like the triangle ADC.
sin 62° = opposite/hypotenuse
opposite = 85 ft
sin 62° = 85/BC
cross multiply
BC sin 62° = 85
BC = 85/sin 62°
BC = 85/0.88294759285
BC = 96.2684543086
BC ≈ 96.27 ft
The angle ACB can be gotten when you subtract 62° and 41° from 180 (angle on a straight line).
Therefore,
∠ACB = 180° - 62° - 41°
∠ACB = 77°
Now let us use the cosine law to find the zip line AB.
c² = a² + b² - 2ab cos C
a = 96.27 ft
b = 99.08 ft
c² = 96.27² + 99.08² - 2 × 96.27 × 99.08 cos 77°
c² = 9267.9129 + 9816.8464 - 19076.8632 cos 77°
c² = 19084.7593 - 19076.8632 × 0.22495105434
c² = 19084.7593 - 4291.36049041
c² = 14793.398810
square root both sides
c = √14793.398810
c = 121.628116856
c ≈ 121. 63 ft
length of the zip line = 121. 63 ft
Related Questions
A set of cards with a letter on each card as shown below are placed into a bag. Howard picks a card at random from the bag.
Determine the probability that the card is not an E
Answers
Answer:
your chances would be 9 out 10 or in fraction form 9/10
Find an equation, in slope-intercept form, that passes through the point (−4,3) with a slope of −3.
Answers
Answer:
y = -3x - 9
Step-by-step explanation:
Equation of line in point slope form is given as:
[tex]y - y_1 = m(x-x_1) \\
y - 3= - 3\{x - (-4)\}\\
y - 3 = - 3(x + 4)\\
y =- 3x - 12 +3\\
y = - 3x - 9\\ is \: the \: required \: equation \\ [/tex]
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Answers
Answer:
You tell them
Step-by-step explanation:
Never stop being postive
You have a 10 gallon jug and a 3 gallon jug. Both jugs are unmarked. You need exactly 5 gallons of water. How can you get it if a water faucet is available?
Answers
Answer:
Step-by-step explanation:
You have a 10 gallon jug and a 3 gallon jug and need exactly 5 gallons of water.
This what you do:
- Fill the 3 gallons jug full and pour into the 10 gallons keg
- Repeat the above a second time making a total of 6 gallons of water in the 10 gallons jug.
- Fill the 3 gallons jug a third time and pour into the 10 gallons jug making 9 gallons
- Fill the 3 gallons jug the fourth time and pour into the 10 gallons jug till full leaving 2 gallons of water remaining in the 3 gallons jug.
- Then empty out the 10 gallons jug and pour the 2 gallons of water in the 3 gallons jug into the 10 gallons jug.
- Then, fill the 3 gallons jug again and pour into the 10 gallons jug holding the 2 gallons of water making a total of 5 gallons of water in the 10 gallons jug.
Hope, that helps!!!
Plz help! Question on picture :)
Answers
Answer:
125 students participated
Step-by-step explanation:
66% + 30% = 96%
100% - 96% = 4%
4% = 5 students
100% ÷ 4% = 25
25 × 5 = 125
125 students participated
Answer:
125 students
Step-by-step explanation:
30+66=96
100-96=4
5 students make up 4%.
100/4=25
25x5=125 students
Write 7/20 as a percent.
By what factor should you multiply the denominator and numerator?
Answers
Answer:
35%
Step-by-step explanation:
Use photomath it tells you everything.
Answer:
You should multiply the numerator and the denominator by 5. 35%
Step-by-step explanation:
7/20*5/5=35/100
35%
To get from fraction to percent you need the denominator to be 100. To get the denominator 20 to 100 you need to multiply by 5. Then we just take the numerator and add a percent symbol.
You should multiply the numerator and the denominator by 5. 35%
Maya has $270. She spends one third on shoes and buys 3 shirts for $12. She spends the remaining amount to buy dresses for $32 each. Determine the number of dresses she buys?
Answers
Answer: 4 dresses
Step-by-step explanation:
Hope you get it right!
The table shows the battery life of four different mobile phones:
Mobile Phone Battery Life
Phone: Battery Life (hours)
A: 20
B: 25
C: 10
D: 18
If 8.45% of the battery life of each mobile phone is used in a day by a typical user, for which mobile phone is 0.8 hour of battery life used in a day?
1. Phone A
2. Phone B
3. Phone C
4. Phone D
Answers
Answer:
phone C
Step-by-step explanation:
since, 8.45% of (×) 10
= 0.845
= 0.8
Answer:
probably phone C
Step-by-step explanation:
Please help ASAP! I will mark BRAINLIEST! Please answer CORRECTLY! No guessing!
Answers
Answer:
C. [tex]b^{27}[/tex]
Step-by-step explanation:
Assume b is a number like 3
([tex]3^{9}[/tex])³=19683³=7625597484987
[tex]3^{24}[/tex]=282429536481
B is definitely wrong. Not even going to try.
[tex]3^{27}[/tex]=7625597484987
D is definitely wrong. Not even going to try.
Complete 8 for 15 points.
Answers
Answer:
756 is evenly divisible by 2, 3, 4, 6, and 9.
Step-by-step explanation:
756 is evenly distributed by the numbers (above).
756/2 = 378756/3 = 252756/4 = 189756/5 = 151.2 756/6 = 126756/8 = 94.5756/9 = 84 756/10 = 75.6 756/25 = 30.24Given: 6|x/3| < 18
Part A: Show the step(s) to get the absolute value expression by itself.
Part B: Write the two equations used to solve the absolute value equation.
Part C: Solve the equations and check your equations.
Answers
Answer:
see below
Step-by-step explanation:
6|x/3| < 18
Divide by 6
6/6|x/3| < 18/6
|x/3| < 3
Now we get two equations, one positive and one negative, remembering to flip the inequality
x/3 < 3 x/3 > -3
Multiply by 3 to isolate x
x/3 *3 < 3*3 and x/3*3 > -3*3
x < 9 and x > -9
Rewriting
-9 < x<9
Check -12
6|-12/3| < 18
6|-4| <18
24<18 False good
Check 0
0<18 true
Check 12
6|12/3| < 18
6|4| <18
24<18 False good
Which situation describes INDEPENDENT events? A) One student is chosen from Classroom A, then a student is chosen from Classroom B. B) One card is chosen from a standard deck, it is set aside, then a second card is drawn. C) One student is chosen from Classroom A, then a second student is chosen from Classroom A. D) Tom chooses a letter of the alphabet, then Beth must choose a different letter from the alphabet.
Answers
Answer:
Step-by-step explanation:
A) One student is chosen from Classroom A, then a student is chosen from Classroom B
the sets for each probability to happen are different. what happen in first clause is unrelated to the second clause
Discussion Topic: As part of their job, meteorologists make weather predictions from data. How accurate are their predictions? What are other scenarios in which you would use data to make a prediction? How would you defend your prediction using data?
Answers
Answer: 1. Not always accurate.
2. A football game.
3. By using the data from the winning percentage against number of games played.
Step-by-step explanation:
Meteorologists are responsible for making weather predictions, but their predictions are always not accurate because they use datas and theory to predict the scenarios of the weather or what it might be. Their predictions are not accurate because of changes in weather or data being used unexpectedly.
A scenario where I would use data to make a prediction could be in a football match or game where you i have a percentage of winning, which depends on how many times the game is played.
The winning percentage gives us the data on the probability of winning the game which would help predict how many times you'll win a game by how many times the game is played.
Find cos x if sin x =0.82.
Answers
Answer:
cosx= 35. Use Trignometrical identity cosx = √1−sin2x . cos x = √1−1625 = √925 = 35 to be the ...
Missing: =0.82 | Must include: =0.82
Step-by-step explanation:
I need some help please!! I'll give brainliest to first answer!!!!!!!!!!!!!
Answers
Answer:
Keith; -5, -12
Step-by-step explanation:
Logic ( Subtract 12 from both sides, then factor it out)
A 25ft ladder is propped against a storeroom. The angle the ladder forms is 50°. How far up the storeroom does the ladder reach?
Answers
Answer:
This means the store room is 19.15ft up
Step-by-step explanation:
The set up of the question will form a right angle triangle.
The length of the ladder will be the hypotenuse of the triangle and the angle the ladder forms will be the angle of elevation. This angle of elevation will face the opposite side of the triangle which is the height of the storeroom directly.
Using the SOH CAH TOA trigonometry identity,
According to SOH;
Sin∅ = opposite/hypotenuse
∅ is the angle the ladder forms
sin50° = x/25
x = 25sin50°
x = 19.15ft
This means the store room is 19.15ft up
The senior classes at High School A and High School B planned separate trips to the indoor climbing gym. The senior class at High School A rented and filled 5 vans and 10 buses with 410 students. High School B rented and filled 10 vans and 12 buses with 556 students. Every van had the same number of students in it as did the buses. How many students can a van carry? How many students can a bus carry?
Answers
Answer:
A van can carry 15 students and a bus can carry 966 students
Evaluate the expression when c= -4.
c² – 5c+2
Answers
Answer:
The answer is 38.
Step-by-step explanation:
You have to substitue c = -4 into the expression :
Let c = -4,
[tex] {( - 4)}^{2} - 5( - 4) + 2[/tex]
[tex] = 16 + 20 + 2[/tex]
[tex] = 38[/tex]
x: 3 5 6 10
y: 45 84 116 372
What is the result if the best fit exponential model for the following data set was used to predict the output when x=15?
A) 593
B) 783
C) 1284
D) 1693
Answers
If there are 3 classrooms that each have 25 desks and there are a total of 87 students, how many more desks need to be added to a 4th classroom, that was originally empty, so that each of the students has a desk to sit in?
Answers
Answer:
12
Step-by-step explanation:
If there are 3 classrooms that each have 25 desks and there are a total of 87 students, how many more desks need to be added to a 4th classroom, that was originally empty, so that each of the students has a desk to sit in?
25 * 3 = 75
87 - 75 = 12
Kendra gets a paycheck of 300 after 5 days of work at this rate how much does she get paid for working 24 days
Answers
Answer:
$1,440; Possible work: Since 300 4 5 5 60, Kendra gets paid $60 per day: 60 3 24 5 1,440. So, she gets paid $1,440 for working 24 daysStep-by-step explanation:
HOPE THIS HELPS
Answer:
1440 = x
Step-by-step explanation:
We can use a ratio to solve
300 dollars x dollars
----------------- = ------------
5 days 24 days
Using cross products
300*24 = 5x
Divide each side by 5
300*24/5 = 5x/5
1440 = x
Find the number, if...
3/8 of it is 24.
Answers
Answer:
64
Step-by-step explanation:
To get the answer, just perform the reverse operation of what the question said. In this case, you would want to multiply by the reciprocal, which is (8/3). So the answer is found by just solving 24*(8/3).
Answer:
The number is 64
Step-by-step explanation:
Let the number be x
3/8 of x = 24
x = 24 ÷ (3/8)
[tex]x=24*\frac{8}{3}\\\\x=8*8[/tex]
x = 64
15 5 6 6 19 4 5 5 3 4 5 19 5 4 6
What is the mean? Round your answer to the nearest tenth.
Answers
sum = 0
while we haven't covered all the numbers, repeat these:
Step 1: sum = sum + (next number)
Step 2: counter = counter + 1
When all numbers are covered: the average is (sum/count)
Juan went out to eat dinner, and the meal cost $60.00. If Juan received an 18% discount, what was the total value of the discount?
Answers
Answer:
The total value of the discount was $10.80.
Step-by-step explanation:
Since we are finding the value of the discount, we just need to find 18% of 60.
We can convert 18% into a decimal.
18%=0.18
Multiply.
0.18*60=10.8
The total value of the discount was $10.80.
A plane slices through the axis of a right circular cone with a height of 4 feet and a radius of 3 feet, as shown below. What is the perimeter of the intersection of the plane and the cone?
Answers
Answer: 37.64
Step-by-step explanation:
Given data:
Height of the cone = 4feet
Radius of the cone = 3feet
Therefore:
Perimeter of a cone = 1/3 * π * r*h
= 1/3 * 22/7 * 3² * 4
= 0.333 * 3.14 * 9 * 4
= 37.64 feet
The perimeter of the The cone and plane is 37.64feet
The area of a rectangular baking sheet is 25 square inches. The base of the sheet is 10 inches. What is the height?
2 and one-half in.
3 in.
3 and one-half in.
250 in.
Answers
Answer:
2 1/2
Step-by-step explanation:
take 25 and divide it by 10 giving you 5/2 but that equals 2.5 and 2.5 equals 2 1/2
2 [tex]\frac{1}{2}[tex] in.
Step-by-step explanation:
PLEASE HELP
For a hypothesis test of H0: p = 0.35 against the alternative Ha: p > 0.35, the z test statistic is found to be 2.45. What can be said about this finding?
A. The finding is significant at α = 0.05, but not at α = 0.01.
B. The finding is significant at α = 0.01, but not at α = 0.05.
C. The finding is significant at both α = 0.05 and α = 0.01.
D. The finding is not significant at α = 0.05 and α = 0.01.
Answers
Answer:
C
Step-by-step explanation:
Is is a one-tailed test
P(z < 2.45) = 0.9929
1 - 0.9929 = 0.0071
Significant at both 0.05 and 0.01 because both are greater than 0.0071
Answer:
The finding is significant at both α = 0.05 and α = 0.01.
Calculate the volume of the solid. Round answer to the nearest hundredth.
Answers
find the value of y squared when y is -9
Answers
Answer:
81
Step-by-step explanation:
-9^2, or -9 times -9 equals 81, the negatives cancel each other out
Your answer would be 81.
The calculation the question is asking us to do is y², but substitute in y for -9. This gives us (-9)². We know that 9² = 81, but (-9)² also equals 81 because when you multiply 2 negative numbers together, the negative sign cancels out.
I hope this helps!
What is the approximate area of the shaded sector in the circle shown below?
A. 31.7 cm^2
B. 5.76cm^2
C. 2.88cm^2
D. 126.7cm^2
Answers
Answer:it’s 31.7 cm^2
Step-by-step explanation:
The approximate area of the shaded sector is 31.7 cm² (Option A).
To find the area of the shaded sector, we need to calculate the fraction of the entire circle that the sector represents and then multiply it by the area of the whole circle.
The formula to find the area of a sector is given by:
Area of sector = (θ/360) * π * r²
where θ is the central angle and r is the radius of the circle.
In this case, the radius (r) of the circle is given as 11 cm, and the central angle (θ) is given as 30 degrees.
Let's calculate the area of the shaded sector:
θ = 30 degrees
r = 11 cm
Area of sector = (30/360) * π * 11²
= (1/12) * π * 121
= π * 10.0833...
Now, we can approximate the value of π as 3.14:
Area of sector ≈ 3.14 * 10.0833...
≈ 31.7 cm²
Therefore, the approximate area of the shaded sector is 31.7 cm².
The correct option from the given choices is A. 31.7 cm².
To know more about sector, refer here:
https://brainly.com/question/12051312
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