Two corners of a triangle have angles of $\frac{π}{3}$ $pi / 3$ and $\frac{π}{2}$ $pi / 2$ . If one side of the triangle has a length of $2$ $2$ , what is the longest possible perimeter of the triangle?

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Two corners of a triangle have angles of $\frac{π}{3}$ $pi / 3$ and $\frac{π}{2}$ $pi / 2$ . If one side of the triangle has a length of $2$ $2$ , what is the longest possible perimeter of the triangle?

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Answer 1 · 2016-08-19T08:01:26

$= 4.732$ $=4.732$

Explanation:

Clearly this is a right angled triangle with one of the two given angles are $\frac{π}{2} and \frac{π}{3}$ $pi/2 and pi/3$ and Third angle is $π - (\frac{π}{2} + \frac{π}{3}) = π - \frac{5 π}{6} = \frac{π}{6}$ $pi-(pi/2+pi/3)=pi-(5pi)/6=pi/6$

One $s i d e = h y p o t e n u s e = 2$ $side=hypoten use =2$ ;So other sides $= 2 sin (\frac{π}{6}) and 2 cos (\frac{π}{6})$ $=2sin(pi/6) and 2cos( pi/6)$

Therefore Perimeter of the triangle $= 2 + 2 sin (\frac{π}{6}) + 2 cos (\frac{π}{6})$ $=2+2sin(pi/6)+ 2cos( pi/6)$

$= 2 + (2 \times 0.5) + (2 \times 0.866)$ $=2+(2times0.5)+(2times0.866)$

$= 2 + 1 + 1.732$ $=2+1+1.732$

$= 4.732$ $=4.732$

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Two corners of a triangle have angles of $\frac{π}{3}$ $pi / 3$ and $\frac{π}{2}$ $pi / 2$ . If one side of the triangle has a length of $2$ $2$ , what is the longest possible perimeter of the triangle?

1 Answer

Explanation:

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Two corners of a triangle have angles of $\frac{π}{3}$ $pi / 3$ and $\frac{π}{2}$ $pi / 2$ . If one side of the triangle has a length of $2$ $2$ , what is the longest possible perimeter of the triangle?