7. Non-Right Triangles

Given two triangles with corresponding angles and side lengths related by the $Law of Sines$, which of the following pairs of triangles can be mapped onto each other using a single translation?

Given that ray $BE$ bisects $\angle ABC$, and $\angle ABE=2x+7°$ and $\angle CBE=5x-8°$, what is the measure of $\angle ABC$?

Which one of the following sets of data does not determine a unique triangle?

a. A = 50°, b = 21, a = 19

b. A = 45°, b = 10, a = 12

c. A = 130°, b = 4, a = 7

d. A = 30°, b = 8, a = 4

In triangle $rst$, $r$ = $58$ cm, $\angle s$ = $48°$ and $\angle t$ = $29°$. Find the length of side $s$, to the nearest centimeter.

In triangle $\mathrm{ABC}$, if angle $A$ measures $100°$ and angle $B$ measures $20°$, what is the measure of arc $\mathrm{BC}$ (the angle at vertex $C$)?

In triangle $ABC$, side $a$ is $7$, side $b$ is $10$, and angle $A$ is $30°$. Angle $B$ is $45°$. Using the Law of Sines, find the length of side $c$. If necessary, write your answer in simplest radical form.

Given that triangle $ABC$ is similar to triangle $AXY$ with a ratio of similarity $3:2$, and that $bc=24$ in triangle $ABC$, what is the length of the corresponding side $xy$ in triangle $AXY$?

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

Which of the following correctly states the Law of Sines for a triangle with sides $a$, $b$, $c$ opposite angles $A$, $B$, $C$, specifically relating a single pair of side and opposite angle?

Given that triangle $ABC$ is similar to triangle $DEF$, which of the following correctly expresses the Law of Sines for these triangles?

In Exercises 33–38, find the area of the triangle having the given measurements. Round to the nearest square unit. C = 102°, a = 16 meters, b = 20 meters

According to the Law of Sines, which triangle below correctly demonstrates that the side opposite the larger angle is the larger side?

Given that line zx bisects angle $\angle wzy$ in triangle wzy, and the measure of angle $\angle yxz$ is $6m-12$ degrees, which of the following could be the value of $m$ if angle $\angle yxz$ is an acute angle?

In triangle $△abc$, which angle's measure is equal to the sum of the measures of $\angle bac$ and $\angle bca$?

In Exercises 1–8, solve each triangle. Round lengths of sides to the nearest tenth and angle measures to the nearest degree.