Two corners of a triangle have angles of $( pi )/ 3$ and $( pi ) / 6$ . If one side of the triangle has a length of $15$ , what is the longest possible perimeter of the triangle?

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Two corners of a triangle have angles of $( pi )/ 3$ and $( pi ) / 6$ . If one side of the triangle has a length of $15$ , what is the longest possible perimeter of the triangle?

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Answer 1 · 2017-10-05T21:56:37

Longest possible perimeter $=70.98$

Explanation:

Given two angles are $pi/3=60^0$ & $pi/6=30^0$
There the third angle $=180-60-30=90^0$
It is a right angle triangle with angles in the ratio of $1:2:3$ and hence the sides in the ratio of $1:sqrt3:2$ where the smallest side is 1. To get the longest perimeter, smallest side 1 should have the length 15.
Perimeter of the triangle is sum of all the three sides.
$=15+15sqrt3+(15*2)=15(1+sqrt3+2)$
$=15*(1+1.732+2)=15*4.732=70.98$

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Two corners of a triangle have angles of $( pi )/ 3$ and $( pi ) / 6$ . If one side of the triangle has a length of $15$ , what is the longest possible perimeter of the triangle?

1 Answer

Explanation:

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Science

Math

Humanities

... and beyond

Two corners of a triangle have angles of ( pi )/ 3 ( pi )/ 3 and ( pi ) / 6 ( pi ) / 6 . If one side of the triangle has a length of 15 15 , 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 $( pi )/ 3$ and $( pi ) / 6$ . If one side of the triangle has a length of $15$ , what is the longest possible perimeter of the triangle?