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barxatty [35]
3 years ago
5

A ladder (line segment AC in the diagram) is leaning against a wall. The distance between the foot of the ladder and the wall (B

C) is 7 meters less than the distance between the top of the ladder and the ground (AB). A-Create an equation that models the length of the ladder (l) in terms of x, which is the length in meters of AB. B-If the length of the ladder is 13 meters, use the equation you wrote to find the distance between the ground and the top of the ladder (AB).

Mathematics
1 answer:
Serga [27]3 years ago
8 0

<em>Greetings from Brasil...</em>

a)

Let's just use Pythagoras

L² = X² + (X - 7)²

<h3>L = √(2X² - 14X + 49)</h3><h3 />

b)

If L = 13, then what is the value of X ???

L² = 2X² - 14X + 49

2X² - 14X - 120 = 0

X = 12  or  X = - 5

<em>(The distance cannot be negative, so X = 12)</em>

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2. In the circle shown, secants PE and PF have been drawn such that mCE  82 , mDF  98 and the ratio 3. In circle O, tangent
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Complete Question

The complete question is shown on the first uploaded image

Answer:

The arc PR is  \theta _{PR}  = 84

Step-by-step explanation:

A descriptive diagram of the diagram given in the question is shown on the first uploaded image

  In the circle tangent  \=  {M \= Q} , secant PE and  chord PF are drawn

given that  \theta _ {MPQ} = 102^o , \theta _{M} =  60^o

   The objective is to determine PR

From the diagram we see that MQ is a straight which implies that the the angle

      \theta_{NPM}  =  180 -102

      \theta_{NPM}  =  78^o

Now looking at triangle NMP we see that

          \theta _{MNP} =  180  -[ \theta_{NMP} + \theta _{NPM}]

         \theta _{MNP} =  180  - [60 + 78 ]

         \theta _{MNP} =  42 ^o

Now the measure of an inscribed angle is half the measure of its  arc intercepted, this statement is the inscribed angle theorem

 So with the knowledge

   Then

           \theta_{RNP} =  \frac{1}{2}  \theta_{PR}

  Looking at the diagram we see that

           \theta _{MNP} = \theta_{RNP} = 42 ^o

             42 = \frac{1}{2}  \theta _{PR}

              \theta _{PR}  = 2  *  42

               \theta _{PR}  = 84

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