Respuesta :
Answer:
Approximately 15.62 feet.
Step-by-step explanation:
The staircase forms a right triangle, with a height of 10 feet and a width of 12 feet. We can solve for the length of the handrail using the pythagorean theorem (considering the handrail would be the hypotenuse of the triangle formed by the staircase).
[tex]a^{2}+b^{2}=c^{2}[/tex]
[tex]10^{2}+12^{2}=c^{2}[/tex]
[tex]244=c^{2}[/tex]
[tex]\sqrt{244} =\sqrt{c^{2}}[/tex]
c = 15.62 ft.
The length of the handrail will be 15.62 feet
What is a right angled triangle?
- Any 2-dimensional figure bounded by 3 sides whose one angle is 90° is called a right angled triangle.
- In a right angled triangle the side opposite to the right angle is the longest and is called the hupotenuse.
How to find the length of the handrail?
According to the problem
- A set of stairs is 10 feet tall and covers a horizontal distance of 12 feet.
The stairs forms a right angled triangle with height 10 feet and base 10 feet.
- The handrail is actually the hypotenuse of the triangle.
Applying the Pythagorean Theorem, we can write,
In a right angled triangle, (hypotenuse)² = (base)² + (perpendicular)²
∴ In the given problem,
(length of the handrail)² = (10)² + (12)²
⇒ (length of the handrail) = [tex]\sqrt{244}[/tex] = 15.62 feet
∴ The length of the handrail = 15.62 feet
Find out more information about 'Right angled triangle' here: https://brainly.com/question/64787
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