The ceiling of Stacy's living room is a square that is 25 ft long on each side. Stacy
knows the diagonal of the ceiling from corner to corner must be longer than 25 ft,
but she doesn't know how long it is.
Solve for the length of the diagonal of Stacy's ceiling in two ways:
(a) Using the Pythagorean Theorem.
(b) Using trigonometry.
Round each answer to the nearest whole number and make sure to show all your
work. (Hint: the answers should be the same!)
Please help !!!
Answers
Answer:
A. 35 ft.
B. 35 ft
Step-by-step explanation:
Please see attached photo for diagram.
A. Determination of the diagonal using pythagorean theorem.
A square has all sides equal. Thus, the diagonal of the square can be obtained as follow:
Ist leg (L₁) = 25 ft
2nd leg (L₂) = 25 ft
Diagonal (d) =?
d² = L₁² + L₂²
d² = 25² + 25²
d² = 625 + 625
d² = 1250
Take the square root of both side
d = √1250
d = 35 ft
B. Determination of the diagonal using trigonometry.
Since all the sides in a square are equal, the angle between each leg will be 90°. Thus, the diagonal will bisect the angle between the two leg equally i.e
Angle between Diagonal and each leg = 90/2 = 45°
Finally, we shall determine the length of the diagonal. This can be obtained as follow:
Angle θ = 45°
Opposite = 25 ft
Hypothenus = d
Sine θ = Opposite / Hypothenus
Sine 45 = 25 / d
0.7071 = 25 / d
Cross multiply
0.7071 × d = 25
Divide both side by 0.7071
d = 25 / 0.7071
d = 35 ft
Related Questions
A photograph measuring 4 inches wide and 5 inches long is enlarged to make a wall mural. If the mural is 150 inches wide, how long is the mural?
A. 120 inches
B. 600 inches
C. 750 inches
D. 187.5 inches
Answers
you would get this by doing the following
150/4 = 37.5
5 x 37.5 = 187.5
In the diagram A, B, and C are the points on the circle. Use the diagram to prove the theorem which states that:
if O is the center of the circle then AÔB = 2Ĉ.
Answers
9514 1404 393
Explanation:
Here's one way to go at it.
Draw segments AB and CO. Define angles as follows. (The triangles with sides that are radii are all isosceles, so their base angles are congruent.)
x = angle OAB = angle OBA
y = angle OAC = angle OCA
z = angle OBC = angle OCB
Consider the angles at each of the points A, B, C.
At A, we have ...
angle CAB = x + y
At B, we have ...
angle CBA = x + z
At C, we have ...
angle ACB = y + z
The sum of the angles of triangle ABC is 180°, as is the sum of angles in triangle ABO. This gives ...
x + x + ∠AOB = (x+y) +(x+z) +(y+z)
∠AOB = 2(y+z) = 2∠ACB
This shows ∠AOB = 2×∠C, as required.
Simplify (3√5 − 5√2 ) (4√5 + 3√2 )
Answers
Answer:
=30−11√1
hope it helped!
Help Please! I've been stuck and options are below!
Answers
Answer:
first question is b second is d
Step-by-step explanation:
7=-1/4+b solve for b
Answers
Answer:
b = 7 1/4
Step-by-step explanation:
7 = -1/4 + b
Add 1/4 to both sides
7 1/4 = b
b = 7 1/4
The Drama Club is showing a video of their recent play. The first showing begins at 2:30 pm. The second showing is scheduled at 5:25 pm with a 30-minute break between showings. How long is the video in hours and minutes?
Answers
Answer:
the video is 4 hours and 25 minutes
Step-by-step explanation:
first you need to subtract 30 minutes from 5:25 giving you 4:55, then you need to find the difference in minutes from 2:30 to 4:55 by subtracting them or just counting because you cannot subtract units of time like they are real numbers. giving you 4 hours and 25 minutes
which triangles are similar?
Answers
Answer:
triangle a and b
Step-by-step explanation:
because its common knowledge
ellus
Find the surface area of the composite figure.
2 cm
7 cm
2 cm
12 cm
12 cm
7 cm
7 cm
SA = [?] cm2
Answers
Answer:
SA = 484 cm²
Step-by-step explanation:
Surface area of the composite figure = surface area of the larger rectangular prism + (surface area of the smaller rectangular prism - base area of the smaller rectangular prism)
✔️Surface are of the larger rectangular prism = 2(LW + LH + WH)
L = 7 cm
W = 7 cm
H = 12 cm
S.A = 2(7*7 + 7*12 + 7*12) = 434 cm²
✔️Surface are of the smaller rectangular prism = 2(LW + LH + WH)
L = 7 cm
W = 2 cm
H = 2 cm
S.A = 2(7*2 + 7*2 + 2*2) = 64 cm²
✔️Base area of the smaller rectangular prism = L*W
L = 7 cm
W = 2 cm
Area = 7*2 = 14 cm²
✅Surface area of the composite figure = 434 + (64 - 14)
= 434 + 50
= 484 cm²
simply log 64 - log 128 + log 32
Answers
Answer:
log(16)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra II
Logarithmic Property [Multiplying]: [tex]\displaystyle log(ab) = log(a) + log(b)[/tex]Logarithmic Property [Dividing]: [tex]\displaystyle \displaystyle log(\frac{a}{b}) = log(a) - log(b)[/tex]Step-by-step explanation:
Step 1: Define
Identify
log(64) - log(128) + log(32)
Step 2: Condense
Logarithmic Property [Dividing]: log(1/2) + log(32)Logarithmic Property [Multiplying]: log(16)Can someone please help me
Answers
Answer:
no no no no no no no no no non no
Help I will brainliest your answer
Answers
Answer: y=12
Step-by-step explanation:
96=8y
96/8=y
12=y
the lee family eats at a restaurant for a total bill of 45$ they decided to give a tip of 18% how much tip will they give
Answers
How to Do it/ Work:
18 * 0.45 = 8.1
Help me PLEASEEEEEEEEEEEEE
Answers
Answer:
B, C, D.
Step-by-step explanation:
These are all statistical questions since these can be answered by collecting data that vary.
There are 5 blue dogs for every 2 green cats. How many green cats are there for 1 blue dog?
Answers
Answer:
2/5
Step-by-step explanation:
The ratio is 5:2 , simplify an you'll get 1:2/5
Need help with this scatter plots question. How do I solve it?
Answers
Answer:
No Trend
Step-by-step explanation:
Scatter plots usually have 1 or 2 outlier points if they're to show a positive or negative trend. There is a kind-of negative trend in the graph, but for me personally, I think the outliers kind of cancel the pattern out since there's way to much other points around it. It can't be constant since constant means that the points have to be in one place, and obviously its not really the case here. Therefore, you're left with a no-trend graph!
Given this graph of average giveaway, what is the best estimate for the expected giveaway value of this game?
graph
A. $1.70
B. $2.50
C. $3.00
D. $3.80
Answers
C
Explanation:
look closely on the x-axis and move the last point all the way to the y-axis it’s in between 2 and 4 so $3.00 move your point from the y-axis and go down it’s either 100 or 0 100 would be $4.00 so i believe it’s C
Answer:
ans c hope it helps u take care have a nice day
Polygon ABCDE ~ Polygon FGHIJ
What is the scale factor of polygon ABCDE to polygon FGHIJ?
Answers
The scale factor of polygon ABCDE to polygon FGHIJ will be 9/2. Then the correct option is C.
What is dilation?Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.
There is no effect of dilation on the angle.
Polygon ABCDE is similar to the Polygon FGHIJ.
Then the scale factor is given as,
Scale factor = 27 / 6
Simplify the equation, then we have
Scale factor = 27 / 6
Scale factor = 9 / 2
The scale factor of polygon ABCDE to polygon FGHIJ will be 9/2. Then the correct option is C.
More about the dilation link is given below.
https://brainly.com/question/2856466
#SPJ1
Similar Triangles
Write the ratio of corresponding sides for the similar triangles and reduce the ratio to lowest terms.
a. 4/15 = 5/12 = 4/15
b. 4/5 = 12/15 = 4/5
c. 4/12 = 5/15 = 1/3
d. 5/4 = 15/12 = 5/4
Please select the best answer from the choices provided
Answers
Answer:
C. 4/12 = 5/15 = 1/3
Step-by-step explanation:
I calculated it logically
Answer:
The answer is A
Step-by-step explanation:
Our environment is very sensitive to the amount of ozone in the upper atmosphere. The level of ozone normally found is 6.8 parts/million (ppm). A researcher believes that the current ozone level is at an insufficient level. The mean of 10 samples is 6.4 ppm with a standard deviation of 1.1. Does the data support the claim at the 0.05 level
Answers
Answer:
The test statistics fall in the critical region and hence null hypothesis is to be rejected.
Step-by-step explanation:
The null hypothesis : H0 : Mean = 6.80
Alternative hypothesis: Ha: Mean is not equal to 6.80
As per the z statistics
z = (x’-mean)/(sigma/sqrt n)
Substituting the given values, we get –
z = 6.4-6.8/(1.1/sqrt 10)
z = -1.149
z test statistics is -1.149
Critical value for two tailed test at 98% confidence is .10749
The test statistics fall in the critical region and hence null hypothesis is to be rejected.
Round 386.565 to the nearest hundredth.
Answers
Hope this helps^^^^
Explanation: the 5 was 5 or higher so you turn it into a 0 and pump the number your rounding up.
Help me pleas. Math is not my thing it read.
Answers
Answer:
74900
Step-by-step explanation:
just multiply the two numbers.
Answer: 74,900
Step-by-step explanation:
multiply
if you add 5 over 8 + 5 over 8.. how do you simplify it and write it as a mixed number?
Answers
Answer:
its equal to 10 over 8
Step-by-step explanation:
then u divide the numerator and denominator by 2 over 2 which will give you 5 over 4
since it's 5 over 4 you 1 whole number which become 1 and 1 over 4
Question 10
Emma played a math game and had the five cards shown.
7
0
-4
2
-10
Her score was the sum of the numbers on these five cards. What was Emma's score?(6.3D)
F 3
G 23
H-5
J Not here
Answers
Answer:
option H: -5
Step-by-step explanation:
[tex]sum \ of \ 7, 0 , -4, 2, -10 = 7 + 0 + (-4) + 2 + (-10)[/tex]
[tex]= (7 +2)+( -4) +( -10)\\=9 - 4 - 10\\=9-14\\=-5[/tex]
What is the value of log6 49?
Round your answer to two places.
Answers
Answer: 2.17
Step-by-step explanation: To get the answer you count the first two numbers on the Decimal Form, starting behind the period.
(2.17206626)
Find x if x : 10 = 10 : x
A) 10 B) 20 C) 16
Answers
Answer:
10 is the correct answer
Answer:
A) 10
Step-by-step explanation:
given,
x:10=10:x
x/10=10/xx²=100x=√100x=10hope it helps.
stay safe healthy and happy.Each cement block weighs 1 1/4 pounds. How much do 8 cement blocks weight in total?
Answers
Answer:
10
Step-by-step explanation:
[tex]1 \frac{1}{4} \times 8 = 10[/tex]
Answer:
10 pounds.
Step-by-step explanation:
1 * 8 + 1/4 * 8
= 8 + 2
= 10 pounds.
(1 point) Solve the initial value problem 8(sin(t)dydt+cos(t)y)=cos(t)sin4(t), for 0
Answers
The equation of a function
y = 2/3x+1/3 find the value of y
when x = -3
when x = 1 1/2
Answers
Answer:
[tex]y = \frac{-5}{3}\\\\y = \frac {4}{3}[/tex]
Step-by-step explanation:
[tex]y = \frac{2}{3} x + \frac{1}{3}\\\\when \ x = -3 \\\\y = \frac{2}{3}(-3) + \frac{1}{3} = -2 + \frac{1}{3} = \frac{-6 + 1}{3}= \frac{-5}{3} \\\\When \ x = 1 \frac{1}{2} = \frac{3}{2}\\\\y = \frac{2}{3} \times \frac{3}{2} + \frac{1}{3} = 1+ \frac{1}{3} = \frac{3 + 1}{3}= \frac{4}{3} \\\\[/tex]
what is your when x = 60?
Answers
Answer:
300
Step-by-step explanation:
Find the y value when x = 60
Looking at the graph when x=60, y= 300
What are the coordinates of the solution of these two linear equations
Answers
Hi there! The solutions of two linear equations can be broken into 3 types:
Infinitely Many SolutionsOne Solution No SolutionThis is from the system of equations where you solve for the y-value and x-value by substitution method or elimination method.
From the question above, the question asks you to find the coordinate of the solution of the equations. But how do we know the coordinate point of the solution if we aren't given any equations? They don't give equatione but they give a graph instead.
Now I would like you to take a look at the graph. You notice that both graphs have one intersect point, right? That point is our solution!
Hence, we can say that an intersection point of two graphs is the solution of both equations.
The graphs intersect each others at (2,1). Thus the answer to this question is (2,1)
Questions can be asked through comment.
Furthermore, an intersection point of two graph is the solution to the equation of the graphs.
Hope this helps, and Happy Learning! :)