A triangle has two corners with angles of $\frac{π}{12}$ $pi / 12$ and $\frac{7 π}{8}$ $(7 pi )/ 8$ . If one side of the triangle has a length of $3$ $3$ , what is the largest possible area of the triangle?

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A triangle has two corners with angles of $\frac{π}{12}$ $pi / 12$ and $\frac{7 π}{8}$ $(7 pi )/ 8$ . If one side of the triangle has a length of $3$ $3$ , what is the largest possible area of the triangle?

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Answer 1 · 2017-04-06T04:05:13

A = 223.478

Explanation:

Sum of 3 amgles of a triangle is $π$ $pi$
So the third angle is $\frac{π}{24}$ $pi/24$
for the largest possible area the side needs to be taken as the smallest side
using sine rule $\frac{a}{sin A} = \frac{b}{sin B} = \frac{c}{sin C}$ $a/sinA =b/sinB=c/sinC$
taking a = 3
we get b = 5.949 and c = 8.796

using the formula for area of a triangle when 3 sides are given:
$A = \sqrt{S \cdot (S - a) \cdot (S - b) \cdot (S - c)}$ $A = sqrt(S*(S-a)*(S-b)*(S-c))$
where S is semiperimeter = 19.745
A = 223.478

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A triangle has two corners with angles of $\frac{π}{12}$ $pi / 12$ and $\frac{7 π}{8}$ $(7 pi )/ 8$ . If one side of the triangle has a length of $3$ $3$ , what is the largest possible area of the triangle?

1 Answer

Explanation:

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A triangle has two corners with angles of π12 pi / 12 and 7π8 (7 pi )/ 8 . If one side of the triangle has a length of 33 , what is the largest possible area of the triangle?

1 Answer

Explanation:

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A triangle has two corners with angles of $\frac{π}{12}$ $pi / 12$ and $\frac{7 π}{8}$ $(7 pi )/ 8$ . If one side of the triangle has a length of $3$ $3$ , what is the largest possible area of the triangle?