7. Non-Right Triangles

In triangle $ABC$, angle $A$ is $30°$, angle $B$ is $45°$, and side $a$ (opposite angle $A$) is $10$ units. Using the Law of Sines, what is the approximate value of side $b$ (opposite angle $B$)?

Given a triangle with vertices $A$, $B$, and $C$, and point $D$ inside the triangle, which of the following must be true for point $D$ to be the orthocenter of the triangle?

Given a circle with points $O$, $A$, and $C$ on its circumference, and major arc $AB$ measures $220°$, what is the measure of angle $\angle OAC$?

In any triangle, which relationship must be true according to the $\mathrm{Law} \mathrm{of} \mathrm{Sines}$?

Which equation can be solved to find one of the missing side lengths in a triangle using the $Law of Sines$?

When using the Law of Sines to solve a triangle, which of the following equations is correct?

In triangle $GHJ$, if $g$ (opposite angle $G$) is $5$ units, $h$ (opposite angle $H$) is $10$ units, and angle $G$ is $30$ degrees while angle $H$ is $60$ degrees, what is the length of line segment $hj$?

Given triangle $FGE$ with sides $f$, $g$, and $e$ opposite angles $F$, $G$, and $E$ respectively, which equation can be used to find the measure of angle $FGE$ using the Law of Sines?

Given two angle measures and the length of the included side in a triangle, how many distinct triangles can be formed?

Fill in the blank(s) to correctly complete each sentence.

A triangle that is not a right triangle is a(n) _________ triangle.

Given a triangle with side lengths $10$ in., $12$ in., and $15$ in., which classification best describes this triangle?

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

If the major arc $JL$ measures $300°$ in circle $M$, which of the following best describes triangle $JLM$?

Which pair of triangles can be proven congruent by the $SAS$ (Side-Angle-Side) Congruence Theorem?

In triangle $FGH$, points $J$ and $K$ are the midpoints of sides $FG$ and $GH$, respectively. If $FH$ has length $10$ and the segment $JK$ is parallel to $FH$, what is the length of $y$, where $y$ is the length of $JK$?