Please help it is due today

A telephone pole has a wire attached to its top that is anchored to the ground. the distance from the bottom of the pole to the

kirza4 [7]

The height of the pole is 96 feet

In mathematics, the Pythagorean theorem, or Pythagoras' theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides. This theorem can be written as an equation relating the lengths of the legs a, b and the hypotenuse c, often called the Pythagorean equation:[1]

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

Create a diagram of the scenario first. You would have a right triangle with a hypotenuse (longest side) of h + 4, a longest leg of h - 68, and one leg of length h to represent the pole.

Set up the equation $h^2 + (h - 68)^2 = (h + 4)^2$ using the Pythagorean theorem ( $a^2 + b^2 = c^2$ ).

$h^2 + (h - 68)^2 = (h + 4)^2$

On simplifying we get

$h^2+h^2-136h+4624 = h^2+8h+16$

$2h^2-136h+4624=h^2+8h+16$

$h^2-144h+4608=0$

Solving using quadratic formula

$h_{1,\:2}=\frac{-\left(-144\right)\pm \sqrt{\left(-144\right)^2-4\cdot \:1\cdot \:4608}}{2\cdot \:1}$

$h_1=\frac{-\left(-144\right)+48}{2\cdot \:1},\:h_2=\frac{-\left(-144\right)-48}{2\cdot \:1}$

h1 = 96 feet , h2 = 48 feet

If height would have been 48 feet then the other side would have a negative value as as 48 - 68 = -20 .

Hence the height of the pole is 96 feet

Learn more about Pythagoras theorem here :

brainly.com/question/343682

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2 years ago

The Haynes family is building an addition to their house that includes a new

elixir [45]

Answer:

Part A

$A_{t}=22(12+w)$

Applying Distributive property: $A_{t}=264+22w$

Part B

$A_{t}=660\ ft^2$

Step-by-step explanation:

 Attached is the model that belongs to this exercise (The model was missing)

The formula for calculate the area of a rectangle is:

$A=lw$

Where "l" is the lenght and "w" is the width.

Part A

Notice that the dimensions of the new bathroom are:

$l=22\ ft\\w=12\ ft$

We do not know the width of the new bathroom, but we know that both rooms will have the same length. Knowing this, we can write an expression for the total area of both rooms by using the Distributive Property:

$A_{t}=22(12+w)$

Applying Distributive property:

$A_{t}=264+22w$

Part B

If the width of the bedroom is 18 feet, you need to substitute this value into the expression $A_{t}=264+22w$ in order to find the total square footage of the two rooms:

$A_{t}=264+22w\\\\A_{t}=660\ ft^2$