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chubhunter [2.5K]
2 years ago
5

An electrician leans an extension ladder against the outside wall of a house so that it reaches an electric box 22 feet up. The

ladder makes an angle of 77^{\circ}
with the ground. Find the length of the ladder. Round your answer to the nearest tenth of a foot if necessary.
Mathematics
1 answer:
jeka57 [31]2 years ago
3 0

The ladder and the outside wall form a right triangle

The length of the ladder is 97.8 feet

<h3>How to determine the length of the ladder?</h3>

The given parameters are:

Distance (B) = 22 feet

Angle of elevation (θ) = 77 degrees

The length (L) of the ladder is calculated using the following cosine ratio

cos(θ) = B/L

So, we have:

cos(77) = 22/L

Make L the subject

L = 22/cos(77)

Evaluate the product

L = 97.8

Hence, the length of the ladder is 97.8 feet

Read more about right triangles at:

brainly.com/question/2437195

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notsponge [240]

Answer:

2.5198421 is yhe answer of 3^√16

6 0
3 years ago
6 less than one-third of a number m is y
nekit [7.7K]

<u><em>Answer:</em></u>

(m×1/3)-6=y

<u><em>Step-by-step explanation:</em></u>

  1. Start with m as the unknown variable.
  2. Now multiple that by 1/3 to find that portion of m. (m×1/3)
  3. Lastly, subtract 6 and set the expression equal to y. (-6=y)
  4. Thus we get our final equation: (m×1/3)-6=y
7 0
2 years ago
Which system of inequalities is represented by the graph?
alexgriva [62]

Answer:

\left\{\begin{array}{l}y\ge -x-6\\ \\ y\le 2x+4\end{array}\right.

Step-by-step explanation:

The diagram shows shaded region which boundary is bounded with two lines.

<u>Equation of the 1st line:</u>

This line passes through the points (-6,0) and (0,-6), so its equation is

\dfrac{x-(-6)}{0-(-6)}=\dfrac{y-0}{-6-0}\\ \\\dfrac{x+6}{6}=\dfrac{y}{-6}\\ \\y=-x-6

<u>Equation of the 2nd line:</u>

This line passes through the points (-2,0) and (0,4), so its equation is

\dfrac{x-(-2)}{0-(-2)}=\dfrac{y-0}{4-0}\\ \\\dfrac{x+2}{2}=\dfrac{y}{4}\\ \\y=2x+4

The origin belongs to the shaded region, so it must satisfy both inequalities, so

-0-6=-6\le 0\Rightarrow correct inequality is -x-6\le y

2\cdot 0+4=4\ge 0\Rightarrow correct inequality is 2x+4\ge y

Note that signsare with notion "or equal to" because lines are solid.

Answer:

\left\{\begin{array}{l}-x-6\le y\\ \\2x+4\ge y\end{array}\right.\Rightarrow \left\{\begin{array}{l}y\ge -x-6\\ \\ y\le 2x+4\end{array}\right.

7 0
3 years ago
Will mark brainliest, please answer correctly!!!
dusya [7]

Answer:

x = 32

Step-by-step explanation:

Since all sides of the triangle are congruent then the triangle is equilateral.

The angles of an equilateral triangle are congruent with measure of 60°

Equate

2x - 4 = 60 ( add 4 to both sides )

2x = 64 ( divide both sides by 2 )

x = 32

8 0
3 years ago
The diagram shows an empty cylindrical container. Ana puts a solid cube of side length 8 cm into the container. She then pours 1
marshall27 [118]

Answer:

<h3><u>Cylinder</u></h3>

\textsf{Volume of a cylinder}=\sf \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}

Given:

  • r = 6 cm
  • h = 18 cm

\begin{aligned}\implies \sf V &= \sf \pi (6)^2(18)\\& = \sf 648 \pi \: cm^3\end{aligned}

<h3><u>Cube</u></h3>

\textsf{Volume of a cube}=\sf x^3\quad\textsf{(where x is the side length)}

Given:

  • x = 8 cm

\begin{aligned}\implies \sf V &= 8^3\\& = \sf 512 \: cm^3\end{aligned}

<h3><u>Volume available to be filled with water</u></h3>

Volume of cylinder - volume of cube

= 684π - 512

= 1532.75204 cm³

    1 litre = 1000 cm³

⇒ 1.5 litres = 1000 × 1.5 = 1500 cm³

As 1500 < 1532.75204, the volume of water poured into the container is smaller than the empty space available in the cylinder.  Therefore, the water will <u>not</u> come over the top of the container.

4 0
2 years ago
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