A painter leans a 30 foot ladder against one wall of a house. At what height
does the ladder touch the wall if the foot of the ladder is 10 feet from the base
of the wall?
Answers
Answer:
20ft
Step-by-step explanation:
The height at which the ladder touch the wall when the ladder is 30 feet long, and the ladder is 10 feet from the base of the wall is 20√2 feet.
What is Pythagoras Theorem?If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:
[tex]|AC|^2 = |AB|^2 + |BC|^2[/tex]
where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).
Consider the diagram below.
We've got:
Length of the ladder = |AC| = 30 ftDistance between ladder's bottom and base of wall = |BC| = 10 ftHeight of wall from base to the point where ladder touches = |AB| is to be known.The wall is usually perpendicular to ground, therefore making 90° angle with it. Thus, ABC is a right angled triangle.
Using Pythagoras theorem in it, we get:
[tex]|AC|^2 = |AB|^2 + |BC|^2\\\\30^2 = |AB|^2 + 10^2\\|AB|^2 = 900 - 100\\\\|AB|^2 = 800\\\\\text{Taking sq. root of both the sides}\\\\|AB| = \sqrt{800} = \sqrt{ (\pm 20\sqrt{2})^2}\\\\|AB| = \pm 20\sqrt{2} \: \rm ft[/tex]
But as length cannot be a negative quantity, so we get:
[tex]|AB| = 20\sqrt{2} \: \rm ft[/tex]
Thus, the height at which the ladder touch the wall when the ladder is 30 feet long, and the ladder is 10 feet from the base of the wall is 20√2 feet.
Learn more about Pythagoras theorem here:
https://brainly.com/question/12105522
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Related Questions
John's goal is to have more than -7−7minus, 7 dollars in his bank account by the end of the month. The variable ddd is the number of dollars in John's bank account at the end of the month
Answers
Answer:
tricky picky question pal,
Step-by-step explanation:
What are the awnswes
Answer:
d > -7.
Step-by-step explanation:
7 times 6=30+? Anyone help please do
Answers
Answer:
12
Step-by-step explanation:
7(6)=30+x
42=30+x
12=x
in triangle ABC, bisectors of angle A and angle C cross each other in point M. find angle ABC if it is half of AMC. (no shape given)
Answers
Answer:
[tex]\angle ABC=60[/tex]
Step-by-step explanation:
[tex][Kindly\ refer\ the\ image\ attachment.]\\We\ are\ given\ that,\\AM\ is\ the\ Angle\ Bisector\ of\ \angle BAC.\\Hence,\\\angle BAM= \angle MAC\\CM\ is\ the\ Angle\ Bisector\ of\ \angle BCA.\\Hence,\\\angle BCM= \angle MCA.\\Also,\\\angle AMC=2 \angle ABC[/tex]
[tex]Now,\\As\ we\ can\ observe\ that,\\\angle BCM + \angle MCA= \angle BCA\\\angle MCA+ \angle MCA= \angle BCA\ [\angle BCM = \angle MCA]\\Hence,\\2 \angle MCA= \angle BCA\\Or, \\\angle MCA=\frac{\angle BCA}{2} \\\\Similarly,\\\angle BAM + \angle MAC= \angle BAC\\\angle MAC + \angle MAC= \angle BAC\\2 \angle MAC = \angle BAC\\Or,\\\angle MAC=\frac{\angle BAC}{2}[/tex]
[tex]Through\ the\ Angle\ Sum\ Property\ of\ a\ Triangle,\ we\ know\ that:\\'The\ Sum\ of\ all\ interior\ angles\ of\ a\ triangle\ is\ 180.'\\Hence,\\In\ \triangle BAC,\\\angle ABC + \angle BCA + \angle CAB=180\\In\ \triangle MAC,\\\angle MAC+ \angle ACM + \angle AMC=180[/tex]
[tex]Hence,\\As\ \angle AMC= 2 \angle ABC, \angle MCA=\frac{\angle BCA}{2}, \angle MAC=\frac{\angle BAC}{2},\\2 \angle ABC+\frac{\angle BCA}{2}+\frac{\angle BAC}{2}=180\\By\ resolving\ the\ denominators,\\\frac{4 \angle ABC+\angle BCA+\angle BAC}{2}=180\\\\By\ comparing\ the\ Sum\ of\ angles\ in\ both\ the\ triangles,\\We\ find\ that\ the\ RHS\ of\ both\ the\ equations\ are\ equal\ i.e.180,\\The\ LHS\ of\ the\ equations\ are\ equal\ too.\\[/tex]
[tex]Hence,\\\angle ABC+ \angle BCA + \angle BAC=\frac{4 \angle ABC+\angle BCA+\angle BAC}{2}\\Hence,\\2(\angle ABC+ \angle BCA + \angle BAC)=4 \angle ABC+\angle BCA+\angle BAC\\Hence,\\2 \angle ABC+ 2 \angle BCA + 2 \angle BAC=4 \angle ABC+\angle BCA+\angle BAC\\Hence,\\2 \angle BCA + 2 \angle BAC-\angle BCA- \angle BAC=4 \angle ABC- 2 \angle ABC\\Hence,\\\angle BCA+\angle BAC= 2\angle ABC[/tex]
[tex]Lets\ get\ back\ to\ the\ Angle\ Sum\ of\ \triangle ABC,\\\angle ABC + \angle BAC + \angle ACB=180\\Hence,\\As\ \angle BCA + \angle BAC= 2 \angle ABC,\\\angle ABC + 2 \angle ABC=180\\Hence,\\3 \angle ABC=180\\\angle ABC=\frac{180}{3}=60[/tex]
Find the midpoint of the line segment with the given endpoints (-4,4),(-2,2)
Answers
Answer:
(-3,3)
Step-by-step explanation:
use the midpoint formula
Find x =
-47
-27
-73
-33
Answers
There are 11 animals in the barnyard with a total of 32 legs. Some are cows and some are ducks.
How many of each animal are there?
Answers
A video store charges $15 for a rental card plus $1.50 per rental. Write a linear equation in
slope-intercept form to model the situation.
Answers
Answer:
15 + 1.50x
Step-by-step explanation:
Help? I’ll mark u brainliest
Answers
Answer:
11 because adjacent is basically next to and NKL is 12
Step-by-step explanation:
5
True or False:
a = 6 is a solution to the inequality a > 6
----
A) True
B
False
Answers
Answer:
False.
Step-by-step explanation:
If we substitute a for 6, the inequality would become 6 > 6. That is not true because 6 cannot be greater than itself.
What is -3 + 4 is it 1, -1, 7 or -7?
Answers
Answer:
The Answer Is 1
Step-by-step explanation:
Because if you take -3+4 you get 1
please answer my question
Answers
Answer:
pppppppppppppointssssss
Line EF is a straight line (180 degrees)...so if angle C inside the triangle is 40, then the measure of angle BCF = 140 degrees (180-40=140)
Hey guys
I need help my brain isn’t working today
Answers
2. x= -6
.
.
.
.
the other 2 i got lazy but need points sorry
Answer:
It's okay my brain doesn't work some days, too.
1. x = -7
2. x = -6
3. x = -1
4. y = 4
Step-by-step explanation:
1. Simply subtract equal and opposite values from positive values and do the same on both sides. Divide the final x value by its coefficient to get 1x = -7
2. Do the same as above AFTER distributing the 4(5 - x)
3. Once again, distribute all values then combine like terms like #1
4. This one uses a fraction to distribute, but it is just like dividing the number by 3 instead of multiplying (6/3 instead of 6 * 3)
Hope I helped!
6) Find the quotient
Answers
1/2 x 1/5 = 1/10
Answer 2 1/10
[2.1 + (9.2 x 3.3)] x 0.8
Answers
Answer:
the answer is 25.96800
A fence post is 12 feet tall. A chain is attached to the top of the fence post and fastened to the ground 9 feet from the base of the fence post. What is the length of the chain?
Answers
Answer:
15 feet
Step-by-step explanation:
Use the Pythagorean theorem which is a^2 + b^2 = c^2
a and b represents the legs of the triangle
c represents the hypotenuse (which is the chain)
Answer: 15ft chain length
Step-by-step explanation: A right triangle is formed from the picture. Using pythagorean theoreom
12^2+9^2=c^2
225=c^2
15=c
need help plz, completely don’t understand :(
Answers
9514 1404 393
Answer:
see attached
Step-by-step explanation:
In each empty table square, fill in the value that is computed by replacing 'n' in the rule to the left with the value of 'n' above that square.
For example:
The upper left empty square will be filled with ...
n -5 . . . . with n replaced by 1
1 - 5 = -4 . . . . the value that goes in the upper left square.
__
Another example:
The lower right square will be filled with ...
4n -3 . . . . with n replaced by 100
4·100 -3 = 400 -3 = 397 . . . . the value that goes in the lower right square
_____
Additional comment
When there are numerous table values to fill, it can be convenient to let a spreadsheet do the calculations. Here, each formula was entered once, then filled to the right.
I do draws a blueprint of a house using the scale 1 in equals 6 ft in the kitchen has a length of 24 ft what is the length of the kitchen on the blueprint
Answers
Answer:
Length of kitchen on blueprint = 4 in.
Step-by-step explanation:
Scale used to draw a blueprint of a house :
6 feet = 1 in.
Therefore, 1 feet = [tex]\frac{1}{6}[/tex] in.
If the length of kitchen = 24 feet
Then the length of kitchen on the blueprint will be
= [tex]\frac{1}{6}\times 24[/tex]
= 4 in.
Therefore, length of kitchen on blueprint is 4 in.
Andrew paid $40 for a pizza. He forgot that he had a coupon for 10% off the pizza. What would the sale price have been if he used his coupon?
Answers
Answer:
The pizza would have been $36
Answer:
The pizza is 36 dollars if he had used the coupon.
Step-by-step explanation:
Pls pls pls help!! And thank you I’m stuckk
Answers
Answer:
C = 12π
Step-by-step explanation:
The circumference (C) of a circle is calculated as
C = πd ( d is the diameter )
Here d = 12, then
C = 12π
Super Grocery Store paid its cashiers $6.75 an hour. Since the store has come under new management, the cashiers make 25% more an hour. How much do the cashiers currently make an hour? Round answer to the nearest hundredth
Answers
Answer:
The current hourly pay is $8.44 approx
Step-by-step explanation:
Step one:
given data
Super Grocery Store paid its cashiers $6.75 an hour
We are told that the cashiers make 25% more an hour
Required
The cashier's current hourly pay
Step two:
the current hourly pay will be
former pay + 25% of former pay
=6.75+0.25*6.75
=6.75+1.6875
$8.437
=$8.44 approx
Simplify:
2 11/12 + 5 1/2 + 3 3/8
Write you answer as a mixed number.
Answers
Answer:
[tex]2\frac{11}{12} +5 \frac{1}{2} + 3\frac{3}{8}[/tex] (write them out and convert them all into mixed fractions)
[tex]\frac{35}{12} + \frac{11}{2} + \frac{27}{8}[/tex] (find the LCD aka least common denominator)
[tex]\frac{70}{24} + \frac{132}{24} + \frac{81}{24}[/tex] (add all numerators together)
[tex]\frac{283}{24}[/tex] (this is improper, so you need to convert back to mixed by dividing)
[tex]11\frac{19}{24}[/tex] (this is your answer)
How to graph 2x + y = 4 ?
Explain steps please !!
Answers
y= -2x+4
this now matches the formula y= mx+c , -2 being m and 4 being c.
c is your y intercept so the graph will go through 4 on the y axis. Then m is the gradient of your graph and because it is negative you know it is going downwards. 2 means that every unit value you go across the x axis the y axis will go down 2.
To find where your graph crosses the x axis you need to make y=0 in your equation which looks like
0=-2x+4
2x=4
x=2
Now you know that your x intercept is 2 so you can draw a line going through 4 on the y axis and 2 on the x axis like my photo.
look at the picture please help
Answers
Answer:
69
Step-by-step explanation:
which number line shows the best solution for n>3
Answers
Answer:
Open circle on 3 and an arrow going to the right of 3
Step-by-step explanation:
Which value for s will make this equation true?
s(11 - s) = 24
Answers
3(11-3)=24
33-9=24
24=24
8(11-8)=24
88-64=24
24=24
14+x = -9
X equals what?
Answers
Answer:
x=−23
Step-by-step explanation:
14+x=−9
Step 1: Simplify both sides of the equation.
x+14=−9
Step 2: Subtract 14 from both sides.
x+14−14=−9−14
x=−23
Answer:
-23
Step-by-step explanation:
14+x =-9
-14 -14
x = -23
I NEED HELP NOW ITS DUE TOMORROW!
A farmer owns a total of 14 acres in land. The land is separated into 5 5/6 equally sized sections. How many acres are in each section?
Write your answer as a mixed number in simplest form.
Answers
Answer:
2 2/5
Step-by-step explanation:
14 divided by 5/6 is 2 2/5
Write an expression for the sequence of operations described below.subtract 4 from the sum of 2 and y
Answers
Answer:
( 2 + y ) - 4
Gracelyn has 3 more children than Ella has. Gracelyn has 9 children.
How any children does Ella have?
Pick an equation and then solve
a3-x=9
b9x=3
c3/x=9 (fraction)
dx+9=3
ex-3=9
f3x=9
gx+3=9
h.x/3=9 (fraction)
Answers
It could simply be 9-3 or 3+x=9
How could Grace handle those children?!? My parents have trouble handling 4 kids
What property does
(3 + 19) – 12 = 3 + ( 19 – 12)
represent?
Answers
Answer:
associative property
Step-by-step explanation: