# 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.

embizze | High School Teacher | (Level 1) Educator Emeritus

Posted on

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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