A ladder reaches a window 8 meters high on a vertical wall. If the ladder is positioned at a 45° angle to the ground, what is its length?(nearest to a whole number)

Correct — B.
Ladder, wall and ground form a right triangle.
The window height, 8 m, is opposite the 45° angle, and the ladder is the hypotenuse.

sin 45° = 8 ⁄ L, and sin 45° = 1⁄√2
So L = 8√2
≈ 8 × 1.414 = 11.31 m

Nearest whole number: 11 m → option (b)

Why the others are wrong

• (a)
  10m — A 10 m ladder at 45° reaches only 10⁄√2 ≈ 7.07 m up the wall, short of the 8 m window.
• (c)
  12m — 12 m is 11.31 rounded up, but 11.31 is nearer 11. A 12 m ladder at 45° would reach 12⁄√2 ≈ 8.49 m, above the window.
• (d)
  13m — 13 m at 45° would reach 13⁄√2 ≈ 9.19 m, more than a metre above the window.

At 45° a right triangle is isosceles: the two legs are equal and the hypotenuse is √2 times a leg.

Here the wall height is one leg, 8 m, so the foot of the ladder is also 8 m from the wall, and the ladder is 8√2 m.

The rider 'nearest to a whole number' settles the rounding: 8√2 ≈ 11.31, which rounds to 11.

Key facts

• sin 45° = cos 45° = 1⁄√2 ≈ 0.707, and tan 45° = 1
• In a 45°-45°-90° triangle, hypotenuse = leg × √2
• √2 ≈ 1.414, so 8√2 ≈ 11.31

Common traps

• Using tan 45° = 1, which gives the foot's distance from the wall, 8 m, not the ladder's length
• Rounding 11.31 up to 12

No directly related past PYQ was found.