Question

shyam saw a stair that was learned at the top of the wall of height {1/√2 - 1} and distance of stairs from bottom of wall was {√2 - 1} help shyam to find the length of the stair​

Answer 1

Answer:

The length of the stair = √(9/2 - 8)

Step-by-step explanation:

Given:

• Shyam saw a stair that was learned at the top of the wall of height (1/√2 - 1).
• Distance of stairs from bottom of wall was (√2 - 1)

To find:

• The length of the stair.

Solution:

Let's understand the concept first! First we will assume that the length of the stair as x.

We know that height of the wall is (1/√2 - 1) and the distance of stairs from bottom of wall is (√2 - 1) which is the base. Like this we will form a right-angled triangle and by using Pythagoras theorem, we can easily find the hypotenuse of a triangle which is nothing but the length of the stair.

Let AB be the height of the wall,

BC be the distance of stairs from bottom of wall and AC be the length of the stair.

By using Pythagoras theorem,

• AC² = AB² + BC²
• AC² = (1/√2 - 1)² + (√2 - 1)²
• AC² = ((1/√2)² + 1² - 2 × 1/√2 × 1 ) + (√2² + 1² - 2 × √2 × 1)
• AC² = (1/2 + 1 - 2/√2 ) + (2 + 1 - 2√2)
• AC² = ((1+2)/2 - 2/√2 ) + (3 - 2√2)
• AC² = (3/2 - 2/√2 ) + (3 - 2√2)
• AC² = 3/2 - 2/√2 + 3 - 2√2
• AC² = 3/2 + 3 - 2√2 - 2√2
• AC² = (3 + 6)/2 - 2√2 - 2√2
• AC² = 9/2 - 2√2 - 2√2
• AC = √(9/2 - 2√2 - 2√2)
• AC = √(9/2 - (2√2 + 2√2))
• AC = √(9/2 - (2√2)²)
• AC = √(9/2 - 4 × 2)
• AC = √(9/2 - 8)

━━━━━━━━━━━━━━━━━━━━━