A triangle has two corners with angles of $\frac{π}{12}$ $pi / 12$ and $\frac{5 π}{8}$ $(5 pi )/ 8$ . If one side of the triangle has a length of $11$ $11$ , what is the largest possible area of the triangle?

Question

A triangle has two corners with angles of $\frac{π}{12}$ $pi / 12$ and $\frac{5 π}{8}$ $(5 pi )/ 8$ . If one side of the triangle has a length of $11$ $11$ , what is the largest possible area of the triangle?

1 Answer

Impact of this question

1306 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-12-08T13:46:26

Largest possible area of the triangle is 171.333

Explanation:

Given are the two angles $\frac{5 π}{8}$ $(5pi)/8$ and $\frac{π}{12}$ $pi/12$ and the length 11

The remaining angle:

$= π - ((\frac{5 π}{8}) + \frac{π}{12}) = \frac{7 π}{24}$ $= pi - (((5pi)/8) + pi/12) = (7pi)/24$

I am assuming that length AB (11) is opposite the smallest angle.

Using the ASA

Area $= \frac{c^{2} \cdot sin (A) \cdot sin (B)}{2 \cdot sin (C)}$ $=(c^2*sin(A)*sin(B))/(2*sin(C)$

Area $= \frac{11^{2} \cdot sin (\frac{7 π}{24} \cdot \frac{sin ((5 π))}{8})}{2 \cdot sin (\frac{π}{12})}$ $=( 11^2*sin((7pi)/24*sin((5pi))/8))/(2*sin(pi/12))$

Area $= 171.333$ $=171.333$

Science

Math

Humanities

... and beyond

A triangle has two corners with angles of $\frac{π}{12}$ $pi / 12$ and $\frac{5 π}{8}$ $(5 pi )/ 8$ . If one side of the triangle has a length of $11$ $11$ , 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 π12 pi / 12 and 5π8 (5 pi )/ 8 . If one side of the triangle has a length of 1111 , 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 $\frac{π}{12}$ $pi / 12$ and $\frac{5 π}{8}$ $(5 pi )/ 8$ . If one side of the triangle has a length of $11$ $11$ , what is the largest possible area of the triangle?