(α)

Let l = length of the ladder

The known side (5 m) is the adjacent side to the 60° angle.

The length of the ladder (l) is the hypotenuse.

The ratio with adjacent and hypotenuse is cosine.

cos(θ) = $\frac{\mathrm{Adjacent}}{\mathrm{Hypothenuse}}$

cos(60°) = $\frac{\mathrm{5\; m}}{\mathrm{l}}$

But cos(60°) = $\frac{1}{2}$

$\frac{1}{2}$ = $\frac{\mathrm{5\; m}}{\mathrm{l}}$

Cross multiply:

l x 1 = 5 m x 2

l = 10 m

Length of the ladder = 10 m

Length of the ladder = 10.0 m (1 d.p.)

(β)

Let h = height of the building to the window

h is the opposite side to the 60° angle.

The adjacent side is known (5 m).

The ratio with opposite and adjacent is tangent.

tan(θ) = $\frac{\mathrm{Opposite}}{\mathrm{Adjacent}}$

tan(60°) = $\frac{\mathrm{h}}{\mathrm{5\; m}}$

But tan(60°) = 1.732

1.732 = $\frac{\mathrm{h}}{\mathrm{5\; m}}$

Multiply both sides by 5 m to get rid of the fraction.

h = 1.732 x 5 m = 8.66 m

Distance between the window and the foot of the building = 8.7 m (1 d.p.)