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 Exercises 1–12, solve each triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. If no triangle exists, state 'no triangle.' If two triangles exist, solve each triangle. C = 50°, a = 3, c = 1

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 $Law of Sines$?