Two corners of a triangle have angles of $\frac{7 π}{12}$ $(7 pi )/ 12$ and $\frac{π}{4}$ $pi / 4$ . If one side of the triangle has a length of $15$ $15$ , what is the longest possible perimeter of the triangle?

Question

Two corners of a triangle have angles of $\frac{7 π}{12}$ $(7 pi )/ 12$ and $\frac{π}{4}$ $pi / 4$ . If one side of the triangle has a length of $15$ $15$ , what is the longest possible perimeter of the triangle?

1 Answer

Impact of this question

1166 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-07-26T07:53:00

The perimeter is $= 65.2 u$ $=65.2u$

Explanation:

enter image source here

The angles are

$ˆ A = \frac{7}{12} π$ $hatA=7/12pi$

$ˆ B = \frac{1}{4} π$ $hatB=1/4pi$

$ˆ C = π - (\frac{7}{12} π + \frac{1}{4} π) = π - (\frac{7}{12} π + \frac{3}{12} π) = \frac{2}{12} π = \frac{1}{6} π$ $hatC=pi-(7/12pi+1/4pi)=pi-(7/12pi+3/12pi)=2/12pi=1/6pi$

To have the longest perimeter, the side $= 15$ $=15$ must be opposite the smallest angle

Therefore,

$c = 15$ $c=15$

Applying the sine rule to the triangle

$\frac{a}{sin ˆ A} = \frac{b}{sin ˆ B} = \frac{c}{sin ˆ C}$ $a/sin hatA=b/sin hatB=c/sin hatC$

$\frac{a}{sin (\frac{7}{12} π)} = \frac{b}{sin (\frac{1}{4} π)} = \frac{15}{sin (\frac{1}{6} π)} = 30$ $a/sin(7/12pi)=b/sin(1/4pi)=15/sin(1/6pi)=30$

So,

$a = 30 sin (\frac{7}{12} π) = 29$ $a=30sin(7/12pi)=29$

$b = 30 sin (\frac{1}{4} π) = 21.2$ $b=30sin(1/4pi)=21.2$

The perimeter is

$P = 15 + 29 + 21.2 = 65.2 u$ $P=15+29+21.2=65.2u$

Science

Math

Humanities

... and beyond

Two corners of a triangle have angles of $\frac{7 π}{12}$ $(7 pi )/ 12$ and $\frac{π}{4}$ $pi / 4$ . If one side of the triangle has a length of $15$ $15$ , what is the longest possible perimeter of the triangle?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

Two corners of a triangle have angles of 7π12 (7 pi )/ 12 and π4 pi / 4 . If one side of the triangle has a length of 15 15 , what is the longest possible perimeter of the triangle?

1 Answer

Explanation:

Related questions

Impact of this question

Two corners of a triangle have angles of $\frac{7 π}{12}$ $(7 pi )/ 12$ and $\frac{π}{4}$ $pi / 4$ . If one side of the triangle has a length of $15$ $15$ , what is the longest possible perimeter of the triangle?