ladder against a wall

Question

A ladder 22 feet long leans against the side of a house. Suppose the angle of elevation is 70 degrees.
a) find the height from the top of the ladder to the ground.
b) find the horizontal distance from the foot of the ladder to the wall.

Answer 1

Here c = 22 and θ = 70°

sinθ = h/c, cosθ = d/c.

sin70 = h/22

Trigonometry table in sin70°= 0.9396 and cos70°= 0.342

0.9396 = h/22

Multiply each side by 22.

h = 22(0.9396) = 20.6712 .

The height from the top of the ladder to the ground is 20.6712 feet.

cos70 = d/22.

0.342 = d/22

Multiply each side by 22.

d = 22(0.342) = 7.524

The horizontal distance from the foot of the ladder to the wall is 7.524 feet.