A triangle has two corners with angles of $\frac{π}{2}$ $( pi ) / 2$ and $\frac{5 π}{12}$ $( 5 pi )/ 12$ . If one side of the triangle has a length of $19$ $19$ , what is the largest possible area of the triangle?

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Answer 1 · 2018-06-09T12:11:44

Largest possible area of triangle is $673.64$ $673.64$ sq.unit.

Angle between Sides $A and B$ $A and B$ is $∠ c = \frac{π}{2} = 90^{0}$ $/_c= pi/2=90^0$

Angle between Sides $B and C$ $B and C$ is $∠ a = \frac{5 π}{12} = 75^{0}$ $/_a= (5 pi)/12=75^0$

Angle between Sides $C and A$ $C and A$ is

$∠ b = 180 - (90 + 75) = 15^{0}$ $/_b= 180-(90+75)=15^0$ For largest area of triangle

$19$ $19$ should be smallest side , which is opposite to the smallest

angle , $/_b :. B=19$ The sine rule states if $A, B and C$

are the lengths of the sides and opposite angles are

$a, b and c$ in a triangle, then: $A/sin a = B/sin b=C/sin c ; B=19$

$:. A/sin a=B/sin b or A/sin 75= 19/sin 15$

$:. A=19*sin 75/sin 15 or A ~~ 70.91$ .

Now we know sides $A=70.91 , B=19$ and their included angle

$/_c = 90^0$ . Area of the triangle is $A_t=(A*B* sin c)/2$ or

$A_t=(70.91*19* sin 90)/2~~ 673.64$ sq.unit

Area of the largest possible triangle is $673.64$ sq.unit [Ans]

A triangle has two corners with angles of ( pi ) / 2 π2 ( pi ) / 2 and ( 5 pi )/ 12 5π12 ( 5 pi )/ 12 . If one side of the triangle has a length of 19 1919 , what is the largest possible area of the triangle?