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umka21 [38]
3 years ago
5

How far from the base of the house do you need to place a 15 foot ladder so that it exactly reaches the top of a 12 foot wall?

Mathematics
2 answers:
Lyrx [107]3 years ago
8 0

A 15 foot ladder needs to be placed at a distance of <u>9 foot </u>from the base of the house so that it exactly reaches the top of a 12 foot wall.

<h2>Further Explanation:</h2><h3>Right triangle </h3>
  • A right triangle is a triangle with one of its angles being 90 degrees or right angle.
  • The triangle has two shorter sides making the right angle and the hypotenuse which is the longest side.
<h3>Scalene triangle</h3>
  • It is a triangle that with sides and angles that are not equal.
<h3>Pythagoras Rule </h3>
  • According to Pythagoras rule, in a right angled triangle if the squares of the shorter sides are added then they are equivalent to the square of the hypotenuse.
  • That is; a^{2} + b^{2} =c^{2}, where a and b are the shorter sides while c is the hypotenuse.

In this case;

  • The ladder, the wall of the house and the ground from the base of the house makes a right angled triangle;

Therefore;

  • Length of the ladder is the hypotenuse which is 15 ft
  • The wall of the house is one of the leg which is 12 ft

We are going to find the distance of the ladder from the base of the house on the ground which is the other leg.

Using Pythagoras theorem;

a^{2} + b^{2} = c^{2}

Taking the horizontal distance of the ladder from the wall as b

Then;

b^{2} = c^{2} -a^{2}

therefore,

b^{2} = 15^{2} -12^{2}

b^{2} = 225 -144

b^{2} = 81

b = \sqrt{81} \\b= 9 ft

Hence; the ladder needs to be placed at a distance of 9 foot from the base of the house.

Keywords: Right triangle, Pythagoras rule

<h3>Learn more about: </h3>
  • Pythagoras theorem: brainly.com/question/13035995
  • Right triangle: brainly.com/question/13035995
  • Application of Pythagoras theorem: brainly.com/question/11638432

Level; High school

Subject: Mathematics

Topic: Pythagoras theorem

GarryVolchara [31]3 years ago
5 0

Answer:

9 ft

Step-by-step explanation:

The ladder is 15 foot

The height the ladder reaches from the bottom of the wall is 12 ft

The distance (x) from the bottom of the wall to the foot of the ladder is:

Applying the Pythagorean theorem;

x = \sqrt{15^2 - 12^2} = 9 ft

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Samuel is 4 1/6 feet tall. His dad is 5 3/4 feet tall.How much taller is Samuels dad then Samuel
Sloan [31]

Answer:

1 7/12

Step-by-step explanation:

Just subtract the fractions if you cant do it by head or paper use a calc so 5 3/4 - 4 1/6= 1 7/12 samuels dad is 1 7/12 taller than samuel.

6 0
2 years ago
Which trigonometric function best describes the graph below?
yanalaym [24]
The function is the Sine Curve

y = sine (x)
8 0
3 years ago
The numbers of teams remaining in each round of a single-elimination tennis tournament represent a geometric sequence where an i
Anit [1.1K]

Answer:

a_n = 128\bigg(\dfrac{1}{2}\bigg)^{n-1}

Step-by-step explanation:

We are given the following in the question:

The numbers of teams remaining in each round follows a geometric sequence.

Let a be the first the of the geometric sequence and r be the common ration.

The n^{th} term of geometric sequence is given by:

a_n = ar^{n-1}

a_4 = 16 = ar^3\\a_6 = 4 = ar^5

Dividing the two equations, we get,

\dfrac{16}{4} = \dfrac{ar^3}{ar^5}\\\\4}=\dfrac{1}{r^2}\\\\\Rightarrow r^2 = \dfrac{1}{4}\\\Rightarrow r = \dfrac{1}{2}

the first term can be calculated as:

16=a(\dfrac{1}{2})^3\\\\a = 16\times 6\\a = 128

Thus, the required geometric sequence is

a_n = 128\bigg(\dfrac{1}{2}\bigg)^{n-1}

4 0
3 years ago
It is believed that 44% of all Americans eat breakfast every day. For a class project, you randomly select Clemson students and
GaryK [48]

Answer:

For this case we want to conduct a test in order to see if the proportion of Clemson students who eat breakfast is different from 0.44 (alternative hypothesis). And the complement would represent the null hypothesis, and the system of hypothesis for this case are:

Null Hypothesis: p =0.44

Alternative hypothesis: p \neq 0.44

Step-by-step explanation:

Previous concepts

A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".  

The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".

The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".

Solution to the problem

For this case we want to conduct a test in order to see if the proportion of Clemson students who eat breakfast is different from 0.44 (alternative hypothesis). And the complement would represent the null hypothesis, and the system of hypothesis for this case are:

Null Hypothesis: p =0.44

Alternative hypothesis: p \neq 0.44

8 0
3 years ago
Sally has decided to spend some time over two days soving math problems. She figures that on the first day she wil be able to so
erastova [34]

A system of equations for this would be

19x + 11y = 273

and

12x + 17y = 283.

X is the amount of minutes to solve one long division problem and y is the amount of minutes to solve a graphing problem.

How To Solve This System of Equations.

Multiply both by 17 and 11 respectively for them to have the greatest common factor for y. So now both equations are:

323x + 187y= 4641

132x + 187y= 3113.

Subtract both equations and you have left:

191x = 1528.

Divide both sides by 191 and you find x.

X = 8.

Answer

It takes Sally 8 minutes to do one Long Division Problem.


Hope this helped. ;)

6 0
3 years ago
Read 2 more answers
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