Trigonometry-2

A ladder 41 meters long is placed with its foot at a distance of 9 meters from

the wall of a house and just reaches the window sill. Find the height

of the window sill and the sine and cotangent of the angle which the

ladder makes with the ground.

Solution: C is the window sill and AC is the ladder.

AB = 9 m; AC = 41 m

From right-angled triangle ABC

BC² = AC² - AB² = 41² - 9²

i.e. BC² = (41 + 9)(41- 9)

= 50 X 32 = 25 X 64

Therefore, BC = 5 X 8 = 40 m

Height of window sill = 40 m

Let Θ be the angle which the ladder makes with the ground

Sin Θ = BC/AC = 40/41

Cot Θ = AB/BC = 9/40