Question

The diagram shows a bridge that can be lifted
to allow ships to pass below. What is the
distance AB when the bridge is lifted to the
position shown in the diagram?
(Note that the bridge divides exactly in half
when it lifts open.)
​

Answer 1

AB = 0.84 m

Step-by-step explanation:

See the attached diagram.

Here, the right triangle Δ APD has AP = 43 m, AD = 6 m and we have to calculate PD.

So, applying Pythagoras Theorem,

AP² = PD² + AD²

⇒ 43² = PD² + 6²

⇒ PD² = 1813

⇒ PD = 42.58 m

Due to symmetry, QC will also be 42.58 m

So, AB = DC = PQ - PD - QC = 86 - 42.58 - 42.58 = 0.84 m (Answer)