Two corners of a triangle have angles of $(3 pi )/ 8$ and $( pi ) / 6$ . If one side of the triangle has a length of $14$ , what is the longest possible perimeter of the triangle?

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Two corners of a triangle have angles of $(3 pi )/ 8$ and $( pi ) / 6$ . If one side of the triangle has a length of $14$ , what is the longest possible perimeter of the triangle?

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Answer 1 · 2017-01-20T06:22:47

Longest possible perimeter of the triangle is $67.63$

Explanation:

As the two angles of a triangle are $(3pi)/8$ and $pi/6$ ,

the third angle is $pi-(3pi)/8-pi/6=(24pi-9pi-4pi)/24=(11pi)/24$

As the smallest angle is $pi/6$ , the perimeter will be longest, if the given side $14$ is opposite it. Let it be $a=14$ and other two sides be $b$ and $c$ opposite angles of $(3pi)/8$ and $(11pi)/24$ .

Now according to sine formula,

$a/sinA=b/sinB=c/sinC$

i.e. $b/sin((3pi)/8)=c/sin((11pi)/24)=14/sin(pi/6)=14/(1/2)=28$ and then

$b=28sin((3pi)/8)=28xx0.9239=25.8692$

and $c=28sin((11pi)/24)=28xx0.9914=27.7592$

and perimeter is $14+25.8692+27.7592=67.6284~~67.63$

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Two corners of a triangle have angles of $(3 pi )/ 8$ and $( pi ) / 6$ . If one side of the triangle has a length of $14$ , what is the longest possible perimeter of the triangle?

1 Answer

Explanation:

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Impact of this question

Science

Math

Humanities

... and beyond

Two corners of a triangle have angles of (3 pi )/ 8 (3 pi )/ 8 and ( pi ) / 6 ( pi ) / 6 . If one side of the triangle has a length of 14 14 , what is the longest possible perimeter of the triangle?

1 Answer

Explanation:

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Impact of this question

Two corners of a triangle have angles of $(3 pi )/ 8$ and $( pi ) / 6$ . If one side of the triangle has a length of $14$ , what is the longest possible perimeter of the triangle?