7. Non-Right Triangles

According to the Law of Sines, under which of the following angle conditions could a triangle exist? Select the correct option.

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

Find B if C = 51.3°, c = 68.3 m, b = 58.2 m

According to the $LawofSines$, which triangles can be mapped onto one another through a sequence of rigid transformations?

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

Find b if a = 165 m, A = 100.2°, B = 25.0°

Solve each triangle ABC that exists.

B = 39.68°, a = 29.81 m, b = 23.76 m

Find the unknown angles in triangle ABC for each triangle that exists.

B = 74.3°, a = 859 m, b = 783 m

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

a = 31, b = 26, B = 48°

$$In the context of the Law of Sines $\mathrm{Law} \mathrm{of} \mathrm{Sines}$ and triangle geometry, if two lines (such as transversals or sides) are not parallel, which types of angles remain congruent?

According to the $\text{Law of Sines}$, which set of angle measures could represent the angles of a triangle?

Which of the following sets of angles can form a triangle?

A painter is going to apply paint to a triangular metal plate on a new building. Two sides measure 16.1 m and 15.2 m, and the angle between the sides is 125°. What is the area of the surface to be painted?

Quadrilateral RSTU is a parallelogram. If angle R measures $x$ degrees and angle S measures $70$ degrees, what must be the value of $x$?

Given a triangle with sides $a$, $b$, $c$ opposite angles $A$, $B$, $C$ respectively, which equation can be used to find $b$ using the Law of Sines?

Solve each triangle ABC that exists.

B = 72.2°, b = 78.3 m, c = 145 m

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