# jordan is standing on a bridge over the Welland Canal. His eyes are 5.1m above the surface of the water. He sees a cargo ship heading straight towards him. from his position, the bow appears at an...

jordan is standing on a bridge over the Welland Canal. His eyes are 5.1m above the surface of the water. He sees a cargo ship heading straight towards him. from his position, the bow appears at an angle of depression 5 degrees and the stern appears at an angle of depression of 1 degree.

a) What is the straight-line distance from the bow to jordan.

b)what is the straight-line distance from the stern to jordan

c) what is the length of the ship from bow to stern.

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### 3 Answers

The bow is the front of the ship, and the stern the rear of the ship.

The angle of depression from Jordan to the bow is `5^@` , so the angle formed by the bridge and his line of sight is `85^@` . If we let the distance from the bow to the bridge be x, then `tan85^@=x/5.1` using the trigonometric relationship `tan="opposite"/"adjacent"` .

Then `x=5.1tan85^@~~58.29` and the distance from the bow to the bridge is approximately 58.29m.

The angle of depression to the stern is `1^@` so letting the distance from the stern to the bridge be y we have `tan89^@=y/5.1==>y=5.1tan89^@~~292.18` m.

The length of the ship is y-x; the length of the ship `L~~292.18-28.29=233.89` m.

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