drawbridge at the entrance to an ancient castle is raised and lowered by a pair of chains. The figure represents the drawbridge when flat. Find the height of the suspension point of the chain, to the nearest tenth of a meter, and the measures of the acute angles the chain makes with the wall and the drawbridge, to the nearest degree.
Answers
Answer:
4.0 meters, ∠C = 39°, ∠A = 51°
Step-by-step explanation:
Firstly, our diagram shows us that the given triangle is actually a right triangle. So we can use the Pythagorean Theorem to solve for the height of the chain:
[tex]a^{2} +b^{2} =c^{2}[/tex]
[tex](3.3)^{2} +b^{2} =(5.2)^{2}[/tex]
[tex]b^{2} =(5.2)^{2}-(3.3)^{2}[/tex]
[tex]b =\sqrt{(5.2)^{2}-(3.3)^{2}}[/tex]
[tex]b=4.0187...[/tex]
[tex]b=4.0 m[/tex]
Now, we can use the Law of Cosines to figure out one of the acute angles:
[tex]c^{2} =a^{2} +b^{2} -2ab(cos(C))[/tex]
[tex](3.3)^{2} =(4.0)^{2} +(5.2)^{2} -2(4.0)(5.2)(cos(C))[/tex]
[tex]cos(C)=\frac{(3.3)^{2}-(4.0)^{2} -(5.2)^{2}}{-2(4.0)(5.2)}[/tex]
[tex]C=cos^{-1}( \frac{(3.3)^{2}-(4.0)^{2} -(5.2)^{2}}{-2(4.0)(5.2)})[/tex]
[tex]C=39.3915...[/tex]
∠C = 39°
And since we know that all angles in a triangle add up to 180°:
∠A + ∠B + ∠C = 180
∠A + 90 + 39 = 180
∠A = 180 - 90 - 39
∠A = 51°
However, you should always review any answers on the Internet and make sure they are correct! Check my work to see if I made any mistakes!
Related Questions
what is the linear equation of a line with a rate of change of -1/2 that passes through the point (0, 4)
Answers
Answer:
y = 9/2 (fraction)
Step-by-step explanation:
y = mx+c
m = slope
c =y -intercept
Therefore, the required equation is:
y = 2x + c
Putting the point (0,4) in it as it lies on a line, we get:
4 = -1/2 + c
Therefore:
c = 9/2
So, y = 9/2
Brainlist pls!
need help asap will give brainly
Answers
Answer:
x = 60
Step-by-step explanation:
So, ever triangle, no matter what shape or size, is always going to equal 180 degrees. You start off by trying to find angle L which is 71. The way you find this is you subratch 109 from 180 which ultimately gives you 71.
180 - 109 = 71
After that you have to add what you already have (49 degrees) with what you just found (71 degrees)
49 + 71 = 120
Now that you have 120, you have to again subtract 180 by 120 to get your answer, 60 degrees. And that's it.
180 - 120 = 60
What is 50% of 98 pls
Answers
The answer is 49 :))
PLEASE HELP NOW!!!!!!!
Answers
Answer: BC
Step-by-step explanation:
I know this because i did this one before your welcome
Rewrite using a single positive exponent
Answers
Step-by-step explanation:
[tex] \frac{ {7}^{4} }{7} = {7}^{4 - 1} = {7}^{3} [/tex]
A wedding reception was
being held at Stefano's
restaurant. They charged
$2.00 per person for
appetizers, $20.00 per
person for the main course
and $250 for the wedding
cake. There were 50 people
at the reception. What was
the total cost of the
reception?
Answers
Answer:
the total cost of the wedding would be: 1,350
Step-by-step explanation:
2×50=100 and 20×50=1,000
100+1,000=1,100
1,100+ 250= 1,350
total for wedding is 1,350
:)
Answer: The answer for this problem is $1350.
Step-by-step explanation:
The first thing you do is to see how much money for the appetizers and the main course did all 50 people pay.
50 x 2 = 100, how much money in total for the appetizers
50 x 20 = 1000, how much money in total for the main course
Once you're done with that! Next, you add the total prices for the appetizers and the wedding cake. Then, you add up the $250, so you get your answer!
$100 + $1000 = $1100
$1100 + $250 = $1350
This is how you get the answer!
What is the value of x in the equation 0.03x − 1.2 = 0.24?
Answers
Answer:
x = 48
Step-by-step explanation:
solved it just now-
The storage box for a flag is in the shape of a triangular prism. What is the surface area of the box?
Answers
*see attachment for the diagram of the triangular prism box
Answer:
528.8 in.²
Step-by-step explanation:
Surface area of triangular prism = 2(BA) + P*H
Area of triangular base (BA) = ½*b*h
b = 24.5 in.
h = 12 in.
BA = ½*24.5*12 = 147 in.²
Perimeter of triangular base = 24.5 + 17.1 + 17.1 = 58.7 in.
Height of prism = 4 in.
Plug in the values into the surface area formula:
Surface area of prism = 2(147) + 58.7*4
= 294 + 234.8
= 528.8 in.²
A teacher is planning a class trip to the aquarium. The aquarium requires 2
chaperones for every 15 students. The teacher plans accordingly and orders a
total of 85 tickets. How many tickets are for chaperones, and how many are for
students? Use the table to help you solve.
Use a table.
(Fill rows as needed.)
kids
chaperones
total
15
2
17
Answers
Answer:
The aquarium requires 2 chaperones for every 15 students. The teacher plans accordingly and orders a total of 85 tickets. How many tickets are for chaperones, ...
Step-by-step explanation:
-3x + -15 = 12
x = __
Answers
Answer:
x=9
Step-by-step explanation:
alright so first we eliminate the -15 and to do that we add 15 on both sides:
-3x-15+15=12+15
-3x=27
Now we divide 3 on both sides to make the equation equal to x
[tex] \frac{-3x}{-3} = \frac{27}{-3} [/tex]
x=9
And that's your answer, you're welcome :)
order from least to greatest 3.2 ,3.14, 19/7, sqrt (14)
Answers
Answer: 19/7 ,3.14, 3.2
Step-by-step explanation: Hope this helps Have a brilliant day of learning!
4х + 1= 3x + 2
does it have no solution one solution or infinitely many solutions
Answers
Step-by-step explanation:
4x-3x=2-1
×=1
that's fine
Find the value of 1.999.... in the form of p
q
where p and q are integers.
Answers
1.999… is exactly the number 2.
Let x = 1.999… . Then 1000x = 1999.999… . Subtract x from this to eliminate the fractional part, and you get
1000x - x = 1999.999… - 1.999…
1000x - x = 1999 - 1
999x = 1998
x = 1998/999 = 2/1 = 2
So p = 2 and q = 1.
1. (10 points) Explain how to factor the following:
A: 3m2 + 4m +1 = 0
B: 16n- 25
C: 20n3 - 15n2 + 4n - 3
D: 864.3 + 4
Answers
Answer:
A. 3m² + 4m + 1 = 0
3m² + 3m + m + 1 = 0
3m (m + 1) + 1 (m + 1) = 0
( 3m + 1 ) (m + 1) = 0
B. 16n - 25
16n = 25
n = 25/16
Solve
15x +4< 26.5
Need help fast pls
Answers
Answer:
x<1.5
explanation: move 4 to other side subtract it with 26.5 then divide it by 15
Answer:.
.
Step-by-step explanation:
Han creates a scatter plot that displays the relationship between the number of items sold, x, and the total revenue, y, in dollars.
Han creates a line of best fit and finds that the residual for the point (12, 1,000) is 75. The point (13, 930) has a residual of -40.
Interpret the meaning of -40 in the context of the problem.
Answers
Answer:
In context of the problem, -40 means that 40 was the difference between the actual data, and the estimated data.
Step-by-step explanation:
Here -40 represent the difference between the actual data and the estimated data.
Given that,
Han creates a line of best fit and finds that the residual for the point (12, 1,000) is 75. The point (13, 930) has a residual of -40.Based on the above information we can say that the -40 shows the difference of data.
Learn more: brainly.com/question/17429689
What is the area of the following circle?
Either enter an exact answer in terms of or use 3.14 for 1 and enter your answer as a decimal.
d = 8
Answers
Answer:
50.24
Step-by-step explanation:
A= pi r^2
A= 3.14 * 4^2
A= 3.14 * 16
A= 50.24
solve for e: 5+4e=25
Answers
Answer:
e = 5
Step-by-step explanation:
The midpoint of GH is (-2,3), and its endpoints are G (g,4) and H (-2,h). What are the values of g and h?
Answers
Answer:
g =-2
h = 2
Step-by-step explanation:
left end middle right end
G(g,4) (-2,3) (-2,h)
A soccer tournament was designed with 512 teams where an eighth of the teams were eliminated after each round. Write a function, f(x), that models the number of teams still in the number of teams still in the tournament after x rounds have been played.
Answers
Answer:
f
Step-by-step explanation:
fsdsdsdwdd
$60,000 is invested for 2 years at a simple interest rate of 5%. how much does the investment earn?
Answers
Answer:
6,000
Step-by-step explanation:
It's correct trust me
How do you find a slope and the Y intercept
Answers
Answer:
Step-by-step explanation:
Typically in a line the y intercept is the point where your graph crosses the y-axis, and the x value is 0 so (0,b) is the y-intercept where y-intercept is b
The slope can be found by finding the rate of change, so the change in y / the change in x
You can also calculate the slope with 2 points so (x1, y1) (x2, y2)
you take the y values and subtract them, then divide by the x values like this:
y2 - y1 / x2 - x1
If a line is going up to the right in Quadrant I then the slope is positive, if the slope of the line goes down in Quadrant IV then the line slope is negative
Slopes of horizontal lines are zero, the slope of a vertical line is undefined
We use the letter m to stand for the slope
In the number 15.42, how is the value of the digit "2" different from the value of the digit "2" in the number 12.54?
Answers
This is crazy
Kiran has 2 & 3/4 pounds of flour. When he divides the flour into equal-sized bags, he fills 4 & 1/8 bags. How many pounds fit in each bag?
Answers
Answer:
The number of pounds that will fit in each bag is 2/3 pounds of flour
Step-by-step explanation:
Here, we want to know the amount of pounds that will fit in each bag
What we have to do here is to divide the total number of pounds of flour, by the number of bags filled
We have this as;
2 3/4 divided by 4 1/8
This is;
11/4 divided by 33/8
= 11/4 * 8/33 = 2/3 pounds
can someone help me with this please - can you also give a step by step not just an answer
Answers
Answer:
The way I was taught to do it is to change value into a total fraction, then multiple the numerators together, multiply the denominators together, and finally reduce as far as possible.
7/9 x 5 2/5 = 7/9 x 27/5 = 189/45 = 4 9/45 = 4 1/5
1 3/4 x 4 1/6 = 7/4 x 25/6 = 175/24 = 7 7/24
Calculate the percentage increase of an item that cost R59.99 in 2020 and R 65.99 in 2021
Answers
Answer:
the answer is of this question R = 10
Answer:
The answer is 6%
Step-by-step explanation:
[tex]65.99 - 59.99 = \frac{6 \times 100}{100} = 6\%[/tex]
2/4 of the sum 17 and 4
Answers
[tex]\frac{2}{4} =\frac{1}{2}[/tex]
[tex]\frac{1}{2}[/tex]×[tex](17+4)[/tex]
[tex]\frac{1}{2}[/tex]×21[tex]=10.5[/tex]
Hope this helped.
Match each number with the value of the number rounded to the nearest hundred. 700800763849738Answer: _________________
Answers
Answer:
7008007638496700
Step-by-step explanation:
if you are rounding near the nearest 100th then it would be 7008007638496700
What is the equation of the line that passes through the point (-3, 4) and has a
slope of 1?
Answers
Answer:
y =1x+4
Step-by-step explanation:
Please answer! I’ll make brainliest
Answers
Answer:
16 feet
Step-by-step explanation:
We are Given that
We have a 34 foot ladder leaning against a 30 foot buildingWe are asked to find the distance of the bottom ladder from bottom of the building.A ladder leaning against a object makes the ladder slanted so that means 34 is our hypotense.
The building height And distance of the bottom of ladder and building is our legs so our formula we use is
[tex] {30}^{2} + {x}^{2} = {34}^{2} [/tex]
[tex]900 + {x}^{2} = 1156[/tex]
[tex] {x}^{2} = 256[/tex]
[tex]x = 16[/tex]