7. Non-Right Triangles

Given triangle ABC with sides $a$, $b$, and $c$ opposite angles $A$, $B$, and $C$ respectively, which of the following correctly expresses the Law of Sines?

In circle O, ST is a diameter. If angle S measures $22.0°$, angle T measures $25.0°$, and angle O measures $25.4°$, what must be the value of x using the Law of Sines?

Given two similar triangles, $ABC$ and $DEF$, where $AB=6$, $AC=8$, $DE=9$, and $DF=x$, what is the value of $x$?

Given triangle $△\mathrm{jkl}$, which of the following triangles is similar to it?

Which of the following triangles demonstrates the Law of Sines by showing that the ratios of the lengths of sides to the sines of their opposite angles are equal ($\frac{a}{sin\left(A\right)}=\frac{b}{sin\left(B\right)}=\frac{c}{sin\left(C\right)}$)?

Given triangle $ABC$ with sides $a$, $b$, $c$ opposite angles $A$, $B$, $C$ respectively, which of the following correctly expresses the Law of Sines?

Given two triangles with sides of lengths $6$, $8$, $x$ and $9$, $12$, $15$, what value of $x$ will make the triangles similar by the SSS similarity theorem? $x=$

Which of the following must be true for two triangles to be congruent by the $SSS$ (Side-Side-Side) criterion?

Given triangle $ABC$, which of the following sets of side lengths could represent the sides of a triangle that satisfies the Law of Sines?

If two triangles are similar, which of the following statements about the $\mathrm{Law} \mathrm{of} \mathrm{Sines}$ is always true for both triangles?

Which of the following pairs of triangles are congruent by the Angle-Angle-Side ($AAS$) criterion according to the Law of Sines ($\frac{a}{sin}=\frac{b}{sin}=\frac{c}{sin}$)?

Which of the following expressions represents an exterior angle of triangle $XYZ$?

In triangle $△\mathrm{klm}$, side $m$ has length $63$ inches, angle $\angle k$ is $24°$, and angle $\angle l$ is $42°$. Find the length of side $l$ to the nearest inch.

Given a triangle with sides of lengths $a$, $b$, and $c$, which formula correctly gives the perimeter of the triangle?

In triangle $DEF$, side $d$ = $8$, side $e$ = $12$, and angle $D$ = $40°$. Using the Law of Sines, what is the approximate measure of angle $F$?