Two corners of a triangle have angles of $\frac{π}{3}$ $( pi )/ 3$ and $\frac{π}{6}$ $( pi ) / 6$ . If one side of the triangle has a length of $5$ $5$ , 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 $\frac{π}{6}$ $( pi ) / 6$ . If one side of the triangle has a length of $5$ $5$ , what is the longest possible perimeter of the triangle?

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Answer 1 · 2016-08-18T16:21:20

$= 11.83$ $=11.83$

Explanation:

Clearly this is a right angled triangle as $π - \frac{π}{3} - \frac{π}{6} = \frac{π}{2}$ $pi-(pi)/3-pi/6=pi/2$
One $s i d e = h y p o t e n u s e = 5$ $side=hypoten use =5$ ;So other sides $= 5 sin (\frac{π}{3}) and 5 cos (\frac{π}{3})$ $=5sin(pi/3) and 5cos( pi/3)$

Therefore Perimeter of the triangle $= 5 + 5 sin (\frac{π}{3}) + 5 cos (\frac{π}{3})$ $=5+5sin(pi/3)+ 5cos( pi/3)$

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

$= 5 + 4.33 + 2.5)$ $=5+4.33+2.5)$

$= 11.83$ $=11.83$

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Two corners of a triangle have angles of $\frac{π}{3}$ $( pi )/ 3$ and $\frac{π}{6}$ $( pi ) / 6$ . If one side of the triangle has a length of $5$ $5$ , what is the longest possible perimeter of the triangle?

1 Answer

Explanation:

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Two corners of a triangle have angles of π3 ( pi )/ 3 and π6 ( pi ) / 6 . If one side of the triangle has a length of 5 5 , 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 $\frac{π}{6}$ $( pi ) / 6$ . If one side of the triangle has a length of $5$ $5$ , what is the longest possible perimeter of the triangle?