Write a formula for r in terms of 0 based on the image below
2 answers:
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X + 3x + 5x = 180
9x = 180
x = 20
So the angles are
20
60 and
100
Let's say longest side is c, its length is 5 and it is opposite angle C.
Using the Law of Sines: http://www.1728.org/trigtut2.htm
c / sin(C) = b / sin (B)
5 / sin (100) = b / sin (60)
5 * sin (60) / sin(100) = side b
5 * 0.86603 / 0.98481 = side b
4.33015 /<span> 0.98481 = side b
side b = </span> <span> <span> <span> 4.3969395112 </span> </span> </span>
<span>Using the Law of Sines Again:
</span><span>c / sin(C) = a / sin (A)
5 / sin (100) = a / sin (20)
5 / </span>0.98481 = a / 0.39073
5 * 0.34202 / 0.98481 = side a
1.7101 <span> <span> <span> </span></span></span>/ .98481 = side a
<span>side a = </span> <span> <span> <span> 1.736477087 </span> </span> </span>
SO, perimeter =
5 (side c) plus
<span> <span> 4.3969395112 </span> (side b) plus
</span><span><span><span>1.736477087 (side a)</span> </span>
</span>
<span> <span> <span> 11.1334165982 </span> </span> </span> TOTAL
<span><span>
</span></span>
9x = 180
x = 20
So the angles are
20
60 and
100
Let's say longest side is c, its length is 5 and it is opposite angle C.
Using the Law of Sines: http://www.1728.org/trigtut2.htm
c / sin(C) = b / sin (B)
5 / sin (100) = b / sin (60)
5 * sin (60) / sin(100) = side b
5 * 0.86603 / 0.98481 = side b
4.33015 /<span> 0.98481 = side b
side b = </span> <span> <span> <span> 4.3969395112 </span> </span> </span>
<span>Using the Law of Sines Again:
</span><span>c / sin(C) = a / sin (A)
5 / sin (100) = a / sin (20)
5 / </span>0.98481 = a / 0.39073
5 * 0.34202 / 0.98481 = side a
1.7101 <span> <span> <span> </span></span></span>/ .98481 = side a
<span>side a = </span> <span> <span> <span> 1.736477087 </span> </span> </span>
SO, perimeter =
5 (side c) plus
<span> <span> 4.3969395112 </span> (side b) plus
</span><span><span><span>1.736477087 (side a)</span> </span>
</span>
<span> <span> <span> 11.1334165982 </span> </span> </span> TOTAL
<span><span>
</span></span>