Question

A ladder leans against a wall at an angle of 60⁰ to the wall. If the foot of the ladder is 10cm away from the wall calculate the length of the ladder

Answer 1

[AI-generated answer — Bot GPT 3.5]

The ladder, the wall, and the ground form a right-angled triangle. The ladder is the hypotenuse of the triangle, the distance from the foot of the ladder to the wall is the opposite side, and the height of the ladder where it touches the wall is the adjacent side.

Given that the angle between the ladder and the wall is 60⁰, we can see that the height of the ladder is the side opposite the angle, and the distance from the foot of the ladder to the wall is the adjacent side.

Using trigonometry, we know that the tangent of an angle in a right-angled triangle is equal to the opposite side divided by the adjacent side:

tan(60⁰) = height / 10

tan(60⁰) = √3

Therefore, height = 10√3 ≈ 17.3 cm

Now we can find the length of the ladder using the Pythagorean theorem:

ladder² = height² + distance²

ladder² = (10√3)² + 10²
ladder² = (300) + 100
ladder² = 400

Therefore, the length of the ladder is √400 = 20 cm.