Trig

**n3_olp** · June 30th 2008, 12:32 AM

A simple question just cant work out which function to use.

A man is on the top of the cliff 125m high. He observes two boats in line with him at angles of depression of 45 degrees and 75degrees. How far are they from each other.

Any help would be great,

Thank You

**Simplicity** · June 30th 2008, 12:47 AM

Originally Posted by n3_olp

A simple question just cant work out which function to use.

A man is on the top of the cliff 125m high. He observes two boats in line with him at angles of depression of 45 degrees and 75degrees. How far are they from each other.

Any help would be great,

Thank You

We are told the height and the angle of depression which the angle down from the horizontal. We have to find the angle between the depression and the height so that we can work out opposite given the angle and the adjacent height.

For the $45^{\circ}$ boat:

Angle between the depression and the height: $90^{\circ} - 45^{\circ} = 45^{\circ}$

$\text{tan}\theta = \frac{\text{Opposite}}{\text{Adjacent}} \implies\text{Opposite} = (\text{tan}\theta ) \times {\text{Adjacent}}$

$\text{Opposite} = (\text{tan}\theta ) \times {\text{Adjacent}} = (\tan(45^{\circ}))(125) = 125m$

For the $75^{\circ}$ boat:

Angle between the depression and the height: $90^{\circ} - 75^{\circ} = 15^{\circ}$

$\text{Opposite} = (\text{tan}\theta ) \times {\text{Adjacent}} = (\tan(1 5^{\circ}))(125) \approx 33.5m$

Therefore the distance between each boat is $125m - 33.5m = 91.5m$

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