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
Hiiioo!! Can someone please help with this❤️❤️❤️
Answers
Answer:
28
Step-by-step explanation
5x7=45
7x7=49
4x7=28
Hope this helps :)
What is the volume of this container?
20 cm
2,125 cm3
5 cm
5 cm
2,000 cm3
5 cm
20 cm
15 cm
125 cm3
1,875 cm3
Answers
Answer:
the answer is C).1875 cm
Step-by-step explanation:
hope it helps bye!!
Find the value for y
Answers
Answer:
y = 18
Step-by-step explanation:
Because it's interior angles are equal, it is an equilateral triangle.
Equilateral triangles have 3 equal sides.
So:
5y - 6 = 4y + 12
reduce:
y = 18
find multiplicative inverse of -13
Answers
Answer:
asdaqwdawdasd
Step-by-step explanation:
Answer:
Step-by-step explanation:
Multiplicative inverse a number 'n' = [tex]\frac{1}{n}[/tex]
Multiplicative inverse of (-13) =[tex]\frac{-1}{13}[/tex]
The waiting time to ride a roller coaster is 1/3 of an hour when 150 people are in line. How
long is the waiting time when 240 people are in line? Write an equation and solve.
Answers
Answer:
[tex] \frac{66}{125} [/tex]
hours
Hope it helped
PLS mark BRAINLIEST
If two angle measurements are 53° and 70,° what must the third angle measurement equal to form a triangle?Please help please?
Answers
Answer:
57 degrees
Step-by-step explanation:
in a triangle the three interior angles always add to 180°
if you add 53 and 70 you get 123
to find the missing angle you would subtract 180 from the two numbers added
180 - 123
so 57 degrees
List a positive and negative number whose absolute value is greater than 3 justify your answer using the answer using the number line
Answers
What is the total surface area?? Please help me I’m confused
Answers
Answer:
216
Step-by-step explanation:
6y - 3 - 2y = -3
(substitution)
Answers
Answer:
y = 0
Step-by-step explanation:
Tyler tried to solve an equation step by step
3(x +4)=-18
Answers
Answer:
x = -10
3(x + 4) = -18
3x + 12 = -18
3x + 12 = -18
3x = -18-12
3x = -30
x= -30/3
x = -10
Step-by-step explanation:
[tex]3(x + 4) = - 18 \\ (x + 4) = \frac{ - 18}{3 } \\ (x + 4) = - 6 \\ x = - 6 - 4 \\ x = - 10[/tex]
Help plzzzzzzzzzzzzzzzz
Answers
Answer: answer is 72 you can get it by either multiplying the height and the base by two and following the formula for area of a triangle or you can divide 36 by two and multiply that by 4
Step-by-step explanation:
Answer:
72 meters
Step-by-step explanation:
Working on 1 triangle at a time
How to find the area of a triangle: Base x Height divided by 2
So: 6 x 6 = 36
36 divided by 2 = 18
Each triangle is 18 meters
18 x 4 triangles = 72 meters
Easy Math question that I dont get. pleaseeee help.
It is due in 5 minutes
Answers
Answer:
First, Third, Fourth, Fifth
Step-by-step explanation:
x² + 2x - 24 = (x + 6)(x - 4) = x² - 4x + 6x - 24 = x² + 2x - 24
True.
x² - 8x + 15 = (x + 5)(x +3) = x² + 3x + 5x + 15 = x² + 8x + 15
False.
3x² + 4x + 1 = (3x + 1)(x + 1) = 3x² + 3x + x + 1 = 3x² + 4x + 1
True.
5x² - 2x - 3 = (5x + 3)(x - 1) = 5x² - 5x + 3x - 3 = 5x² - 2x - 3
True.
4x² - 49 = (2x - 7)(2x + 7) = 4x² + 14x - 14x - 49 = 4x² - 49
True.
First, Third, Fourth, Fifth
2. Write the numbers as follows:a. 914,532,000in scientific notation.
Answers
Answer:
9.14532 x 10^8
Step-by-step explanation:
please mark brainiest
please give 5 stars
thank you
The value of x is ?
Answers
Steps:
(3x + 12) + x = 180
3x + 12 + x = 180
4x + 12 = 180
4x = 180 - 12
4x = 168
x = 168/4
x = 42
Check:
(3x + 12) + x = 180
3x + 12 + x = 180
3(42) + 12 + 42 = 180
126 + 12 + 42 = 180
180 = 180 ✅
I would appreciate the brainliest if this was correct and had helpful & clear steps! :)
8( 3x – 7) simplified
Answers
Answer:
the answer will be 24x−56
Step-by-step explanation:
have a nice day !!
if your looking for the answer to x just divide -56 by 24
ILL GIVE BRAINLIST TO FIRST REAL ANSWER PLS HELP
what would the domain and range be
Answers
Answer:
2nd point
Step-by-step explanation:
Is 4/5 greater or less than 45/100 how do you know
Answers
Answer:
4/5 is grater than 45/100
Step-by-step explanation:
Why?
because in percentage you make the bottom # a 100 one of them already has that and when it has 100 on the bottom it tells you that the top # is the percentage so 45/100 is 45%
now to make 4/5 a percentage what times 5 = 100?
20 does
so you times the top and bottom by 20
4*20= 80
now your fraction is 80/100 (top # tells you the %)
it's 80%
80% is grater than 45%
Answer:
4/5 is greater than 45/100.
Step-by-step explanation:
In order to figure it out, you need to make both fractions have common denominators. In order to do that, you figure out this:
5 times what equals 100? It's 20.
With fractions in this situation, whatever you do to the top, you have to do to the bottom. So, you multiply 4 times 20, which is 80.
In the end, you would end up with these two fractions:
80/100 and 45/100.
Obviously, 80/100 is greater than 45/100. In the beginning, 80/100 was originally 4/5. Therefore, 4/5 is greater than 45/100.
Please consider giving me brainliest if this helped you! :)
BC
Round your answer to the nearest hundredth.
А
65°
6
B
?
Answers
Answer:
90
Step-by-step explanation:
The missing value is 2.56 to the nearest hundredth.
What are the trigonometric identities?Equations using trigonometric functions that hold true for all possible values of the variables are known as trigonometric identities.
We have a right-angled triangle.
And cos(θ) = Adjacent leg / hypotenuse
cos(65°) = The missing value / 6
The missing value = cos(65°) x 6
The missing value = 0.4226 x 6
The missing value = 2.56 to the nearest hundredth.
Therefore, the value is 2.56.
To learn more about the trigonometric identities;
https://brainly.com/question/24377281
#SPJ2
What is the total surface area??? HELP IM CONFUSED
Answers
Answer:
bottom: 12 x 12 = 144
1st triangle: (12 x 8)/2 = 48
2nd triangle: 48
3rd triangle: 48
4th triangle: 48
144 + 48 + 48 + 48 + 48 = 336 cm squared
If a sales person receives a commission of 12% of sales what is the sales person commission on a $250,000 sale
Answers
Answer:
$30,000
Step-by-step explanation:
250000 * 0.12 = 30000
Find the distance between the points (-3,14) and (4,-10)
Answers
Answer:
The answer is -3.4. If you have to round it, round it down to 3.
Step-by-step explanation:
1 A home improvement store purchases $300 worth of materials. They charge a 55% markup. For how much will the materials be sold?
Answers
(300*1.55)
Solve liner equation for they variable
3x-5(x+6)=-2x-2(5+10)
Answers
Answer:
all numbers
Step-by-step explanation:
3x - 5(x + 6) = -2x -2(5 + 10)
Distribute on both sides.
3x - 5x - 30 = -2x - 10 - 20
Add 2x to both sides.
-2x - 30 = -2x - 30
-30 = -30
Since we get a true statement after only doing legal steps to solve the equation, the equation has an infinite number of solutions.
Answer: all numbers
Which of the following are solutions to the inequality below? TELL ME ALL THE ONES THAT ARE RIGHT.
Answers
Answer:
f = 100 and f = 65
Step-by-step explanation:
[tex]\frac{5}{5} \geq 9 = 1 \geq 9[/tex]
[tex]\frac{100}{5} \geq 9 = 20 \geq 9[/tex] ←
[tex]\frac{20}{5} \geq 9 = 4 \geq 9[/tex]
[tex]\frac{65}{5} \geq 9 = 13 \geq 9[/tex] ←
I hope this helps! May I please have brainliest? :)
Question 5
3 pts
(6.03)
How many variable terms are in the expression 3x3y + 5x2 + y + 9? (Input a
numeric value only.) (3 points)
Question 6
4 nts
Answers
Answer:
2
Step-by-step explanation:
Rewrite the following expression using exponents
1/16
Answers
Answer:
6.25 * 10^-2
Step-by-step explanation:
hmmmmmmmmm
I need help with this, it's due in 15 mins-
Mrs. Carver recorded how much time you and your classmates spent working on helping her with the science lab on Friday. The number of hours each student spent is shown below.
1, 1, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 7
She wants you to find the mean, mode, and median of the given data. How did you solve each part?
Answers
Answer:
Mean: 3.5263157894737
Median: 3
Mode: 3
Step-by-step explanation: The mode is 3 because the mode is for which number pops up the most, which is 3.
I got the median by crossing out 8 from the left and the right of the number set and got 3 as the last number.
I got the mean by adding up all the numbers and divided it by the amount of numbers in the set.
...........................
Answers
Answer:
............................
Step-by-step explanation:
which inequality represents all values for x for which the quotient below is defined? square root of 8x squared divided by the square root of 2x
Answers
1/5 of a box of erasers and youneed to share with 3 people including yourself what fraction of the box would each person get
Answers
— x. — = —
4. 5. 20
1/20 is the answer