Find out the answer to "The 5 feet wall stands 28 ft froom..."

High School
Geometry
Trigonometry
Non-right triangles and trigonometry

bobbie71G

Answered question

2021-09-09

The 5 feet wall stands 28 ft froom the building. Find the length of the shortest straight beam that will reach to the side of the building from the ground outside the wall.

Answer & Explanation

Brighton

Skilled2021-09-10Added 103 answers

From similar triangles,

x = 6

(28 + x) = h

H = \frac{28 + x}{x} \times 6

Now, from the

△ A B C

A C^{2} + B C^{2} = A B^{2}

L^{2} = {(x + 28)}^{2} + {(\frac{28 + x}{x} \times 6)}^{2}

\frac{d L}{d x} = 0

2 L \times \frac{d L}{d x} = \frac{d}{d x} (x^{2} + 28^{2} + 56 x + (\frac{x^{2} + 28^{2} + 56}{x^{2}} \times 36))

2 L \times \frac{d L}{d x} = 0 = 2 x + 0 + 56 + 0 + (28^{2} \times 36 x \times \frac{- 2}{x^{3}}) + 56 \times 36 x (- \frac{1}{x^{2}})

2 x + 56448 (- \frac{1}{x^{3}}) - \frac{2016}{x^{3}} = 0

2 x^{4} - 56448 - 2016 x = 0

X = 14 \times 3762 or x = - 11 \times 377

The shortest possible length is

14 \times 3762 .

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