Find Minimum Distance-->Law of Sines

mathxyz

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A 54-foot entrance ramp makes an angle of 4.3 degrees with the level ground. To comply with the most recent wheelchair-accessibility guidelines, the ramp must be extended from point S to point T, so that it makes an angle of, at most, 3 degrees with the level ground. What is the minimum distance from the point on the ground at which the incline of the old ramp begins to the point on the ground where the new ramp must begin? Approximate your answer correct to the nearest inch.

I must find the minimum distance from point S to point T. So, I will say that X = the distance from point S to point T.

This is another law of sines questions. I don't know how to use the law of sines to find the minimum distance between point S and point T. Help...
 
Let S be the high point of the ramp, R be the low point of the ramp and T be the new low point of the ramp.

The angle between RS and the horizontal is 4.3º making angle TRS 175.7º.

Angle STR is 3º.

This makes angle TSR 1.3º.

Side RS is 54 feet.

From the Law of Sines, TR/[sin/_(TSR)] = 54/sin3º

SOlve for TR.

By the same method, solve for the new ramp length is needed.
 
Hey

Denis,

What's wrong? Why did you type 7g4boa5oat5yp8p5y8py5??????
 
I typed characters representing a "swear";
I was swearing at whoever made up that problem!
 
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