Trig: A triangle has a side of length 1, a side of length 4 and an angle of 30◦

s179

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3. A triangle has a side of length 1, a side of length 4 and an angle of 30◦.

(a) Explain carefully why there are precisely two possible such triangles. [7 marks]
(b) In each case determine the third side length and the other two angles of the triangle.[28 marks]


so i calculated the two angles for triangle 1 and found them to be 7.18 and 142.82. ive tried calculating the angles for triangle 2 and keep getting a negative angle, not sure what im doing.
Please help.
 

tkhunny

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What you have not stated is where the angle is in relation to the two sides. I'm guessing the angle is NOT between the two sides, but you didn't say that.

Please show your layout. How did you conclude what you have concluded?

Do you know that \(\displaystyle sin(\alpha) = \sin(\pi - \alpha)\)?
 

Dr.Peterson

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3. A triangle has a side of length 1, a side of length 4 and an angle of 30◦.

(a) Explain carefully why there are precisely two possible such triangles. [7 marks]
(b) In each case determine the third side length and the other two angles of the triangle.[28 marks]


so i calculated the two angles for triangle 1 and found them to be 7.18 and 142.82. ive tried calculating the angles for triangle 2 and keep getting a negative angle, not sure what im doing.
Please help.
I think you have copied the entire problem, and there is no picture; so it is essentially asking you to try putting the 30 degree angle in each of the three possible positions, and determine that one of them is not in fact possible, while the other two are. For example, if AB = 1 and BC = 4, the 30 degree angle might be at A, or B, or C.

You have evidently tried two positions, and solved one but found the second to be impossible. That's just right! Now just try the third position.

But you'll have to tell us more about your work if you need help. What do you mean by "triangle 1" and "triangle 2"? And what work gave you that negative angle?
 
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