7. Non-Right Triangles

Which of the following statements is true for triangle $LNM$ according to the Law of Sines?

A straight ladder of length $L$ leans against a vertical wall, forming an angle $\theta$ with the ground. According to the Law of Sines, what is the proper distance from the feet of the ladder to the wall?

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?

Given triangle ABC with $A=30°$, $B=45°$, and side $a=10$, use the Law of Sines to find the length of side $b$.

Which equation correctly represents the Law of Sines for a triangle with sides $a$, $b$, $c$ opposite angles $A$, $B$, and $C$?

Given triangle $yxz$ with side $yx$ = $3.5$ in, side $xz$ = $5.3$ in, and side $yz$ = $6.4$ in, what is the perimeter of the triangle?

In triangle $LNP$, the length of side $LN$ is $28$ centimeters. If angle $P$ is $30°$ and angle $N$ is $60°$, what is the length of side $LP$?

Which composition of transformations will create a pair of similar, but not congruent, triangles?

Given that $m\angle A+m\angle B=m\angle B+m\angle C$ in triangle $\mathrm{ABC}$, which of the following must be true?

Given triangle $GFE$, which equation can be used to find the measure of angle $GFE$ using the Law of Sines?

Given two triangles $ABC$ and $DEF$ where $\angle A=\angle D$, $\angle B=\angle E$, and $\frac{AB}{DE}=\frac{BC}{EF}$, which triangles in the diagram are congruent?

Which of the following statements correctly describes the requirement for two triangles to be proven similar by the $SAS$ (Side-Angle-Side) similarity theorem?

Which of the following sets of numbers could represent the three sides of a triangle according to the Law of Sines ($\frac{a}{A}=\frac{b}{B}=\frac{c}{C}$)?

Given two triangles, $△STU$ and $△XYZ$, if $△STU$ is congruent to $△XYZ$, which of the following statements about their corresponding sides and angles is true according to the Law of Sines?

In the context of the Law of Sines, which of the following has a measure that is equal to the sum of the measures of the interior angles of a triangle?