The points of triangle are
.
Let u be the vector from
to
as follows:
(Write component form of vector)
(Substitute:
)
(Simplify)
(Write magnitude formula)
(Substitute:
)
(Simplify)
Let v be the vector from
to
as follows:
(Write component form of vector)
(Substitute:
)
(Simplify)
(Write magnitude formula)
(Substitute:
)
(Simplify)
Let w be the vector from
to
as follows:
(Write component form of vector)
(Substitute:
)
(Simplify)
(Write magnitude formula)
(Substitute:
)
(Simplify)
The vectors are
.
The angle C between these vectors is
.
(Apply dot product:
)
(Substitute
)
(Simplify)
(Simplify)
(Multiply each side by
)
(Use calculator)
The vectors are
.
The angle B between these vectors is
.
(Apply dot product:
)
(Substitute
)
(Simplify)
(Simplify)
(Multiply each side by
)
(Use calculator)
The remaining angle
.
The interior angles of triangle are
.