A triangle has two corners with angles of $\frac{π}{4}$ $( pi ) / 4$ and $\frac{7 π}{12}$ $( 7 pi )/ 12$ . If one side of the triangle has a length of $6$ $6$ , what is the largest possible area of the triangle?

Question

A triangle has two corners with angles of $\frac{π}{4}$ $( pi ) / 4$ and $\frac{7 π}{12}$ $( 7 pi )/ 12$ . If one side of the triangle has a length of $6$ $6$ , what is the largest possible area of the triangle?

1 Answer

Impact of this question

1301 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-05-31T06:18:09

Largest possible Area of triangle $A_{t} = 24.6$ $color(green)(A_t = 24.6$

Explanation:

$ˆ A = \frac{π}{4}, ˆ B = \frac{7 π}{12}, ˆ C = π - \frac{π}{4} - \frac{7 π}{12} = \frac{π}{6}$ $hat A = pi/4, hat B = (7pi)/12, hat C = pi - pi/4 - (7pi)/12 = pi/6$

To get largest area, side of length 6 should correspond to least angle $ˆ ˆ C = \frac{π}{6}$ $hat hat C = pi/6$

As per Law of Sines, $\frac{a}{sin A} = \frac{c}{sin C}$ $a / sin A = c / sin C$

$a = \frac{6 \cdot sin (\frac{π}{4})}{sin (\frac{π}{6})} = 8.49$ $a = (6 * sin (pi/4)) / sin (pi/6) = 8.49$

Area of triangle $A_{t} = (\frac{1}{2}) a c sin B$ $A_t = (1/2) a c sin B$

$A_{t} = (\frac{1}{2}) \cdot 8.49 \cdot 6 \cdot sin (\frac{7 π}{12})$ $A_t = (1/2) * 8.49 * 6 * sin ((7pi)/12)$

Largest possible area of triangle $A_{t} = 24.6$ $color(green)(A_t = 24.6$

Science

Math

Humanities

... and beyond

A triangle has two corners with angles of $\frac{π}{4}$ $( pi ) / 4$ and $\frac{7 π}{12}$ $( 7 pi )/ 12$ . If one side of the triangle has a length of $6$ $6$ , what is the largest possible area of the triangle?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

A triangle has two corners with angles of π4 ( pi ) / 4 and 7π12 ( 7 pi )/ 12 . If one side of the triangle has a length of 66 , what is the largest possible area of the triangle?

1 Answer

Explanation:

Related questions

Impact of this question

A triangle has two corners with angles of $\frac{π}{4}$ $( pi ) / 4$ and $\frac{7 π}{12}$ $( 7 pi )/ 12$ . If one side of the triangle has a length of $6$ $6$ , what is the largest possible area of the triangle?