Question

Two sides of a triangle are 16 and 7. Find the size of the angle x (in radians) formed by the sides that will maximize the area of the triangle

Answer 1

Itʻs 1am and I am pretty much brain dead. I know the answer to this somewhere, but I canʻt think, lol

Answer 2

@Astrophysics I know u know tis bruthah

Answer 3

ty @ikram002p :)

Answer 4

like this ?

Answer 5

i suppose yes, now area of triangle with respect to x is

\(\Large ~Area ~=\frac{1}{2}~side1~\times ~side2~ \times \sin x\)

as x is the angle btw side1 and side2
ok so far ?

Answer 6

so we know side1=16 and side2=7
area=1/2*7*16*sin x=56 sin x

we need maximum of area, note that
0<=sin x<=1
0<=56 sin x <= 56
0<= area <= 56 which gives u maximum area of what?

Answer 7

i suppose maximum area is 56 right ? that gives us

area =56 sin x
56 =56 sin x
sin x =56/56=1
sin x =1

which angle x that have sin of 1 ??