#11.

54.7 ft

Step-by-step explanation:

The question given above can be summarised in the attached photo.

u = Initial distance from the building

x = final distance from the building

y = distance moved from the initial point.

First, we shall determine the value of 'u'. This can be obtained as follow:

Opposite = 200 ft

Adjacent = u

Angle θ = 45°

Tan θ = Opposite / Adjacent

Tan 45 = 200 / u

Cross multiply

u × Tan 45 = 200

u × 1 = 200

u = 200 ft

Next, we shall determine the value of 'x'. This can be obtained as follow:

Opposite = 200 ft

Adjacent = x

Angle θ = 54°

Tan θ = Opposite / Adjacent

Tan 54 = 200 / x

Cross multiply

x × Tan 54 = 200

x × 1.3764 = 200

Divide both side by 1.3764

x = 200 / 1.3764

x = 145.3 ft

Finally, we shall determine the value of 'y'. This can be obtained as follow:

u = 200 ft

x = 145.3 ft

y =?

u = x + y

200 = 145.3 + y

Collect like terms

y = 200 – 145.3

y = 54.7 ft

Thus, the person walked 54.7 ft