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!
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6y - 3 - 2y = -3
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Answer:
y = 0
Step-by-step explanation:
The value of x is ?
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Steps:
(3x + 12) + x = 180
3x + 12 + x = 180
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4x = 168
x = 168/4
x = 42
Check:
(3x + 12) + x = 180
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I would appreciate the brainliest if this was correct and had helpful & clear steps! :)
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Answer:
the answer is C).1875 cm
Step-by-step explanation:
hope it helps bye!!
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] ←
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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
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Answers
Answer:
2
Step-by-step explanation:
If a sales person receives a commission of 12% of sales what is the sales person commission on a $250,000 sale
Answers
Answer:
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Step-by-step explanation:
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Hiiioo!! Can someone please help with this❤️❤️❤️
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Answer:
28
Step-by-step explanation
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7x7=49
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Hope this helps :)
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.
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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! :)
The waiting time to ride a roller coaster is 1/3 of an hour when 150 people are in line. How
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Answer:
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hours
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PLS mark BRAINLIEST
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Answer:
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Step-by-step explanation:
Answer:
Step-by-step explanation:
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Tyler tried to solve an equation step by step
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Answers
Answer:
x = -10
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Step-by-step explanation:
Answer:
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Step-by-step explanation:
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Answer:
............................
Step-by-step explanation:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
have a nice day !!
if your looking for the answer to x just divide -56 by 24
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Answers
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Step-by-step explanation:
Because it's interior angles are equal, it is an equilateral triangle.
Equilateral triangles have 3 equal sides.
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Answers
Answer:
57 degrees
Step-by-step explanation:
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BC
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65°
6
B
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Answers
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90
Step-by-step explanation:
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Answer:
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Step-by-step explanation:
please mark brainiest
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— x. — = —
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Answers
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