A triangle has two corners with angles of $\frac{π}{4}$ $pi / 4$ and $\frac{π}{8}$ $pi / 8$ . If one side of the triangle has a length of $8$ $8$ , what is the largest possible area of the triangle?

Question

A triangle has two corners with angles of $\frac{π}{4}$ $pi / 4$ and $\frac{π}{8}$ $pi / 8$ . If one side of the triangle has a length of $8$ $8$ , what is the largest possible area of the triangle?

1 Answer

Impact of this question

1245 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-03-12T00:50:46

32+16 $\sqrt{2}$ $sqrt2$

Explanation:

To create a triangle with maximum area, we want the side of length $8$ $8$ to be opposite of the smallest angle. Let us denote a triangle $DeltaABC$ with $angleA$ having the smallest angle, $frac(pi)(8)$ , or $22.5$ . Thus, $BC=8$ .

From here, we may find the final angle, ( $180-45-22.5=112.5$ ), and apply law of sines to find side $AB$ .

$frac(sin(22.5))(8)=frac(sin(112.5))(x)$ , where $x$ is the length of $AB$ .

Now, we may find the area of the triangle through the formula $Area=frac(1)(2)ab sin(C)$ , or $frac(1)(2)AB*BC sin(B)=32+16sqrt2$ .

Science

Math

Humanities

... and beyond

A triangle has two corners with angles of $\frac{π}{4}$ $pi / 4$ and $\frac{π}{8}$ $pi / 8$ . If one side of the triangle has a length of $8$ $8$ , 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 pi / 4 π4 pi / 4 and pi / 8 π8 pi / 8 . If one side of the triangle has a length of 8 88 , 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 $\frac{π}{8}$ $pi / 8$ . If one side of the triangle has a length of $8$ $8$ , what is the largest possible area of the triangle?