Two corners of a triangle have angles of $\frac{π}{2}$ $( pi )/ 2$ and $\frac{π}{6}$ $( pi ) / 6$ . If one side of the triangle has a length of $8$ $8$ , what is the longest possible perimeter of the triangle?

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Two corners of a triangle have angles of $\frac{π}{2}$ $( pi )/ 2$ and $\frac{π}{6}$ $( pi ) / 6$ . If one side of the triangle has a length of $8$ $8$ , what is the longest possible perimeter of the triangle?

1 Answer

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Answer 1 · 2017-12-12T02:42:56

$24 + 8 \sqrt{3}$ $24+8sqrt3$

Explanation:

the 3 angles: $\frac{π}{2}, \frac{π}{3}, \frac{π}{6}$ $pi/2,pi/3,pi/6$
in order for the sides to be the greatest, we need 8 to be opposite of the smallest angle.
thus, the other sides will be $8 \sqrt{3} and 16$ $8sqrt(3) and 16$ (30,60,90 triangle)
thus the perimeter will be $8 + 8 \sqrt{3} + 16 = 24 + 8 \sqrt{3}$ $8+8sqrt(3)+16=24+8sqrt3$

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Two corners of a triangle have angles of $\frac{π}{2}$ $( pi )/ 2$ and $\frac{π}{6}$ $( pi ) / 6$ . If one side of the triangle has a length of $8$ $8$ , what is the longest possible perimeter of the triangle?

1 Answer

Explanation:

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Two corners of a triangle have angles of ( pi )/ 2 π2 ( pi )/ 2 and ( pi ) / 6 π6 ( pi ) / 6 . If one side of the triangle has a length of 8 8 8 , what is the longest possible perimeter of the triangle?

1 Answer

Explanation:

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Two corners of a triangle have angles of $\frac{π}{2}$ $( pi )/ 2$ and $\frac{π}{6}$ $( pi ) / 6$ . If one side of the triangle has a length of $8$ $8$ , what is the longest possible perimeter of the triangle?