7. Non-Right Triangles

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 $F$?

In triangle $△\mathrm{klm}$, $l=210$ inches, $\angle k=116°$, and $\angle l=11°$. Find the length of $m$ to the nearest inch.

Which of the following correctly expresses the Law of Sines for triangle XYZ with sides $x$, $y$, $z$ opposite angles $X$, $Y$, and $Z$ respectively?

Given triangle $ABC$ with angles $A$, $B$, and $C$, which of the following triangles could ∤ be similar to triangle $ABC$?

Given triangle $△\mathrm{jkl}$, which equation could be used to find $\angle j$ using the Law of Sines?

Triangle $ABC$ has vertices $A$, $B$, and $C$. Under which transformation(s) will the length $AB$ remain equal to $A\text{'}B\text{'}$ after the transformation?

Given two triangles, $△abc$ and $△adc$, can they be proven congruent by the Side-Side-Side (SSS) criterion? Choose the best explanation.

Which of the following correctly states the Law of Sines for triangle $ABC$ with sides $a$, $b$, $c$ opposite angles $A$, $B$, $C$?

Given a circle with radius $r$ = $6$ and an intercepted arc length of $4\pi$, what is the measure of the central angle in radians?

Given two triangles, $△\mathrm{ONM}$ and $△\mathrm{SRQ}$, where side $\mathrm{ON}$ corresponds to $\mathrm{SR}$ and side $\mathrm{NM}$ corresponds to $\mathrm{RQ}$, if $\mathrm{ON}=16$, $\mathrm{NM}=x$, $\mathrm{SR}=20$, and $\mathrm{RQ}=25$, what value of $x$ will make the triangles similar by the SAS similarity theorem?

In parallelogram LMNO, if angle M measures $30°$ and angle N measures $40°$, what is the measure of angle L?

Given triangle $ABC$ with angles $A$, $B$, and $C$, and corresponding opposite sides $a$, $b$, and $c$, which of the following sets of side lengths could represent a triangle according to the Law of Sines?

In triangle $FGH$, an angle bisector from vertex $G$ is perpendicular to side $FH$. If $FG=8$ and $GH=16$, what is the length of $FH$?

Given two right triangles where one leg measures $5$, the hypotenuse measures $13$, and the other leg measures $x$, for the triangles to be congruent by the Hypotenuse-Leg (HL) theorem, what must be the value of $x$?

Which of the following conditions must be true for two right triangles to be congruent by the Hypotenuse-Leg ($\mathrm{HL}$) theorem?