7. Non-Right Triangles

A straight ladder of length $L$ leans against a vertical wall, forming an angle $\theta$ with the ground. According to the Law of Sines, what is the proper distance from the feet of the ladder to the wall?

Given two triangles with sides of lengths $6$, $8$, $x$ and $9$, $12$, $15$, what value of $x$ will make the triangles similar by the SSS similarity theorem?

Given triangle ABC with $A=30°$, $B=45°$, and side $a=10$, use the Law of Sines to find the length of side $b$.

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

Given triangle $yxz$ with side $yx$ = $3.5$ in, side $xz$ = $5.3$ in, and side $yz$ = $6.4$ in, what is the perimeter of the triangle?

In triangle $LNP$, the length of side $LN$ is $28$ centimeters. If angle $P$ is $30°$ and angle $N$ is $60°$, what is the length of side $LP$?

Use the Law of Sines to find the angle $B$ to the nearest tenth of a degree.

Which composition of transformations will create a pair of similar, but not congruent, triangles?

Given that $m\angle A+m\angle B=m\angle B+m\angle C$ in triangle $\mathrm{ABC}$, which of the following must be true?

An engineer wants to measure the distance to cross a river. If $B=30\(\degree\)$, $a=300$$ft$, $C=100\(\degree\)$ find the shortest distance (in $ft$) you’d have to travel to cross the river.

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

Given two triangles $ABC$ and $DEF$ where $\angle A=\angle D$, $\angle B=\angle E$, and $\frac{AB}{DE}=\frac{BC}{EF}$, which triangles in the diagram are congruent?

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?