7. Non-Right Triangles

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.

Solve the triangle: $b=5,c=3,A=100\degree$.

Solve the triangle: $a=5$, $b=15$, $c=13$.

Solve each triangle. See Examples 2 and 3.

a = 3.0 ft, b = 5.0 ft, c = 6.0 ft