7. Non-Right Triangles

To find the distance AB across a river, a surveyor laid off a distance BC = 354 m on one side of the river. It is found that B = 112° 10' and C = 15° 20'. Find AB. See the figure.

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In Exercises 39–40, find h to the nearest tenth.

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Which of the following pairs of triangles are congruent by the Angle-Side-Angle (ASA) criterion according to the Law of Sines?

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

Given triangle $VUW$ with side $v$ opposite angle $V$, side $u$ opposite angle $U$, and side $w$ opposite angle $W$, if $v=7$, $u=10$, and $W=30°$, what are the measures of angles $V$ and $U$ (rounded to the nearest degree)?

Given triangle $lko$ with sides $lk$ and $om$, for which value of $x$ does $lk=om$? Choose the correct value of $x$ from the options below.

Given triangle ABC with sides $a$, $b$, and $c$ opposite angles $A$, $B$, and $C$ respectively, which expression represents the approximate length of side $a$ using the Law of Sines?

In triangle $△\mathrm{lmn}$, side $l$ is $170$ inches, angle $\angle m$ is $121°$, and angle $\angle n$ is $40°$. Find the length of side $n$ to the nearest inch.

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 possible triangle according to the Law of Sines?

Given a triangle where $a$ = $7$, $b$ = $10$, and angle $A$ = $30°$, use the Law of Sines to determine the type of triangle that can be formed.

Given that $m\angle \mathrm{efg}=27°$ and $m\angle \mathrm{gfh}=65°$, what is $m\angle \mathrm{efh}$ in triangle $efg$?

Four students each select three pieces labeled with side lengths and angle measures: Don chooses $a=7$, $A=30°$, $B=60°$; Margo chooses $a=5$, $A=100°$, $b=2$; Sonji chooses $a=8$, $A=45°$, $b=6$; Liam chooses $a=3$, $A=80°$, $b=5$. According to the Law of Sines, which student chose pieces that can be used to construct a triangle?

Which of the following combinations of measurements could form a triangle according to the $Law of Sines$?

Given triangle $△\mathrm{qrs}$ is similar to triangle $△\mathrm{xyz}$, which of the following ratios is equal according to the Law of Sines?