Two corners of a triangle have angles of $\frac{π}{6}$ $pi / 6$ and $\frac{π}{2}$ $pi / 2$ . If one side of the triangle has a length of $6$ $6$ , what is the longest possible perimeter of the triangle?

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Two corners of a triangle have angles of $\frac{π}{6}$ $pi / 6$ and $\frac{π}{2}$ $pi / 2$ . If one side of the triangle has a length of $6$ $6$ , what is the longest possible perimeter of the triangle?

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Answer 1 · 2016-08-16T16:26:34

$= 14.2$ $=14.2$

Explanation:

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

One $s i d e = h y p o t e n u s e = 6$ $side=hypoten use =6$ ;So other sides $= 6 sin (\frac{π}{3}) and 6 cos (\frac{π}{3})$ $=6sin(pi/3) and 6cos( pi/3)$

Therefore Perimeter of the triangle $= 6 + 6 sin (\frac{π}{3}) + 6 cos (\frac{π}{3})$ $=6+6sin(pi/3)+ 6cos( pi/3)$

$= 6 + (6 \times 0.866) + (6 \times 0.5)$ $=6+(6times0.866)+(6times0.5)$

$= 6 + 5.2 + 3)$ $=6+5.2+3)$

$= 14.2$ $=14.2$

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Two corners of a triangle have angles of $\frac{π}{6}$ $pi / 6$ and $\frac{π}{2}$ $pi / 2$ . If one side of the triangle has a length of $6$ $6$ , what is the longest possible perimeter of the triangle?

1 Answer

Explanation:

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Two corners of a triangle have angles of $\frac{π}{6}$ $pi / 6$ and $\frac{π}{2}$ $pi / 2$ . If one side of the triangle has a length of $6$ $6$ , what is the longest possible perimeter of the triangle?