7. Non-Right Triangles

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?

Given that the major arc $JL$ of a circle measures $300°$, which of the following best describes triangle $JLM$ inscribed in the circle with points $J$, $L$, and $M$ on the circumference?

Point D is the incenter of triangle BCA. If $\angle \mathrm{FDG}$ = $136°$, what is the measure of angle $\angle \mathrm{BCA}$?

Given that an equilateral triangle and an isosceles triangle share a common side, and the triangle $ABC$ is equilateral, what is the measure of angle $\angle ABC$ in degrees?

Given the Law of Sines, could $a$ and $b$ be the side lengths of a triangle if $a=3$ and $b=7$ and the angle opposite $a$ is $80°$ and the angle opposite $b$ is $40°$?

Which of the following pairs of triangles can be proven congruent using the $\mathrm{Law} \mathrm{of} \mathrm{Sines}$?

A ship is sailing due north. At a certain point the bearing of a lighthouse 12.5 km away is N 38.8° E. Later on, the captain notices that the bearing of the lighthouse has become S 44.2° E. How far did the ship travel between the two observations of the lighthouse?

Determine the number of triangles ABC possible with the given parts.

a = 50, b = 26, A = 95°

Use the law of sines to find the indicated part of each triangle ABC.

Find b if C = 74.2°, c = 96.3 m, B = 39.5

Given triangle $ABC$ where $A$ and $B$ are on straight lines $l$ and $m$ respectively, and the measure of angle $A$ is $43°$ and angle $B$ is $47°$, what is the measure of angle $y$ (angle $C$) in degrees?

Find the area of each triangle ABC.

A = 42.5°, b = 13.6 m, c = 10.1 m