7. Non-Right Triangles

Given the vertices of a triangle at $(0,0)$, $(5,0)$, and $(2,4)$, use the Law of Cosines to find, correct to the nearest degree, the three angles of the triangle.

Which of the following triangles can you use the Law of Cosines to solve for a missing side?

Given two triangles, $\mathrm{ABC}$ and $\mathrm{XYZ}$, for which pair of triangles is $cos\left(b\right)$ equal to $cos\left(z\right)$?

In triangle $∆ghi$, side $h$ is $820$ inches, angle $\angle g$ is $102°$, and angle $\angle h$ is $10°$. Find the length of side $g$ to the nearest inch.

Which of the following sets of three numbers can represent the side lengths of an obtuse triangle?

In triangle $△wxy$, side $y$ is $940$ inches, angle $\angle y$ is $100°$, and angle $\angle w$ is $38°$. Find the length of side $w$ to the nearest inch.

Given two lines with direction vectors $(3,4)$ and $(5,12)$, use the Law of Cosines to find the acute angle between the lines.

In triangle $MLN$, if side $MN$ is $20$ units, side $LN$ is $24$ units, and the included angle $\angle MLN$ is $60°$, what is the length of chord $ML$?

In a quadrilateral, what is the sum of the measures of all four interior angles?

In triangle $△abc$, $b=620$ cm, $\angle c=106°$ and $\angle a=48°$. Find the length of $a$, to the nearest centimeter.

Given a right triangle with sides $a$, $b$, and hypotenuse $c$, which equation can be used to solve for $c$ using the Law of Cosines?

In triangle $BCD$, which is isosceles with $BC$ congruent to $BD$, what is the measure of angle $CBD$ if angle $C$ is $20°$? Choose the correct answer.

In triangle $\mathrm{ABC}$, if side $\mathrm{AB}$ has length $b$, side $\mathrm{BC}$ has length $a$, and the angle at vertex $C$ is $\gamma$, what is the length of side $\mathrm{AC}$ according to the Law of Cosines?

A surveyor wishes to find the distance across a river while standing on a small island. If she measures distances of $a=30m$ to one shore, $c=60m$ to the opposite shore, and an angle of $B=100\degree$ between the two shores, find the distance between the two shores.

Use the Law of Cosines to find the angle $C$, rounded to the nearest tenth.