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3 years ago

When a stepladder is placed as shown, is it possible for the lower ends of the ladder to be 12 feet apart? Explain

Mathematics

1 answer:

nataly862011 [7]3 years ago

5 0

Answer:

No, with the guides in between the two ladders, it is not possible for the lower ends of the ladder to be up to 12 feet apart

Step-by-step explanation:

The given parameters are;

The length of two sides of the step ladder = 12 feet

The maximum value allowable for the included angle between the two 12 feet ladders = 58°

Therefore, the maximum value of the third side facing the included angle is given as follows;

let "a" represent the maximum value of the third side formed by the distance apart of the lower end of the ladder, by cosine rule, we have;

a² = 12² + 12² - 2 × 12 × 12 × cos(58°) = 135.383251901

∴ a = √(12² + 12² - 2 × 12 × 12 × cos(58°)) ≈ 11.64

The maximum value of the third side formed by the distance apart of the lower end of the ladder = a ≈ 11.64 feet < 12 feet

Therefore, it is not possible for the lower ends of the ladder to be up to 12 feet apart.

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When a stepladder is placed as shown, is it possible for the lower ends of the ladder to be 12 feet apart? Explain​

When a stepladder is placed as shown, is it possible for the lower ends of the ladder to be 12 feet apart? Explain