Calculate angle through which Roberta swings.

Trigonometric ratios and functions, the unit circle, inverse trig functions, identities, trig graphs, etc.
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little_dragon
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Calculate angle through which Roberta swings.

Postby little_dragon » Sat Feb 14, 2009 8:33 pm

The ropes of a swing are 4 metres long, and the seat is 30 cm above the ground when it s t its lowest point. When Roberta uses the swing, the weat reaches a height of 2 metres above the ground on each side of the vertical. Calculate the angle APB through which she swings.

The picture of the swinging looks kind of like an upside down ice cream cone. The ropes are attached at P (the pointy end of the cone) and she swings the rope from A to B. The rounded part-of-a-circle part at the bottom is her path, and is the arc I have to find the angle for.

I've drawn lines from A to B and from P down to the ground. I've labelled where the vertical line crosses AB as X and where it reaches the arc as Y. I know that XY has to be 2 - 0.3 = 1.7, so PX has to be 4 - 1.7 = 2.3. Also, they gave me that AP = BP = 4.

What next? :confused:

anonmeans
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Re: Calculate angle through which Roberta swings.

Postby anonmeans » Sat Feb 14, 2009 9:39 pm

Label half of the angle you need to find as "a". So let APX = a. Then solve cos(a) = 2.3/4 to find a. Multiply by 2 to find the angle you need.

Let me know if that doesn't make sense. 8-)

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little_dragon
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Re: Calculate angle through which Roberta swings.

Postby little_dragon » Sun Feb 15, 2009 2:15 pm

I just learned about sines and cosines, and forgot about doing the cos-1 button to find the angle. Thanks! :wave:


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