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bearhunter [10]
3 years ago
7

A 24 ft ladder is positioned next to a house for window cleaning. The manufacturer recommends the ladder rest at an angle of 76°

with respect to the ground for safe operation. How far away from the house should the ladder be positioned to ensure the recommended angle of 76°? Round your answer to the nearest foot.
A 76 degree angle of elevation is drawn. The line from the horizontal axis to the vertical axis measures 24 units.

Enter your answer in the box.
Mathematics
1 answer:
Butoxors [25]3 years ago
8 0

Answer:

6 feet

Step-by-step explanation:

cos = adj/hyp

cos76 = adj/24

multiply both sides by 24

24 * cos76 = adj

5.806125494392025 = adj

Rounded

6 feet

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Using the given information, give the vertex form equation of each parabola.
Amanda [17]

Answer:

The equation of parabola is given by : (x-4) = \frac{-1}{3}(y+3)^{2}

Step-by-step explanation:

Given that vertex and focus of parabola are

Vertex: (4,-3)

Focus:(\frac{47}{12},-3)

The general equation of parabola is given by.

(x-h)^{2} = 4p(y-k), When x-componet of focus and Vertex is same  

(x-h) = 4p(y-k)^{2}, When y-componet of focus and Vertex is same

where Vertex: (h,k)

and p is distance between vertex and focus

The distance between two points is given by :

L=\sqrt{(X2-X1)^{2}+(Y2-Y1)^{2}}

For value of p:

p=\sqrt{(X2-X1)^{2}+(Y2-Y1)^{2}}

p=\sqrt{(4-\frac{47}{12})^{2}+((-3)-(-3))^{2}}

p=\sqrt{(\frac{1}{12})^{2}}

p=\frac{1}{12} and p=\frac{-1}{12}

Since, Focus is left side of the vertex,

p=\frac{-1}{12} is required value

Replacing value in general equation of parabola,

Vertex: (h,k)=(4,-3)

p=\frac{-1}{12}

(x-h) = 4p(y-k)^{2}

(x-4) = 4(\frac{-1}{12})(y+3)^{2}

(x-4) = \frac{-1}{3}(y+3)^{2}

8 0
3 years ago
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