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hatteras yachts
hatteras yachts
Trig functions????


I have a problem in math and I'm not entirely sure how to do it......

The cape Hatteras lighthouse rises 208 ft above sea level. From the top the keeper observes a yacht and a barge on along the same line of sight. The angle of depression for the yacht is 12 degrees and 30 minutes, the angle of depression of the barge is 20 degrees. The keeper thinks he two vessels are at least 300 ft apart. Is they are less than 300 ft, she plans to sound the horn. How far apart are the vessels?Does she have to sound the horn.

The problem is I don't know what the adjacent side is. I use tan of 20 degrees is equal to 208 over something? And then what do I do?

Help!!!?!?!

This is x vs. y so we're using tangents.

'Depression' means below the sight line, which means the same angle when you want to find the elevation of the lighthouse from the yacht and the barge. When you're looking DOWN at someone at a given angle, they're looking UP at you at the same angle.

Depression of 12° 30' = 12.5°
The depression of the barge is greater than that of the yacht; the barge is closer than the yacht.

tan = opposite/adjacent

208/(distance from lighthouse to yacht) = tan(12.5°)

208/(distance from lighthouse to barge) = tan(20°)

In general, 208/(distance to object X) = tan(depression of object X)

distance to object X = 208/tan(depression of object X)

For the yacht, distance = 208/tan(12.5°) ≅ 938.2 feet
For the barge, distance = 208/tan(20°) ≅ 571.5 feet

Separation is 938.2 - 571.5 ≅ 366.8 feet, so no need to sound the horn.



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