Question

A bridge is 100 metres wide. From the one end of the bridge a person spots a boat with an angle of depression of 35 degrees. From the other end of the bridge another person spots the same boat with an angle of depression of 65 degrees. Find the vertical height of the bridge.

Answer 1

- The sketch of the scenario is

- We can find the value of x using the sine rule. This is done below:

`\begin{gathered} (x)/(\sin115)=(100)/(\sin30) \\ \\ \therefore x=(100*\sin115)/(\sin30) \\ \\ x=181.26156m \end{gathered}`

- After finding the value of x, we can apply SOHCAHTOA, as follows:

`\begin{gathered} \sin35=(h)/(x)=(h)/(181.26156) \\ \\ \therefore h=181.26156*\sin35 \\ \\ h=103.9674m \end{gathered}`

Final answer

The vertical height of the bridge is 103.9674m