7. Non-Right Triangles

Given triangle ABC with sides $a$, $b$, and $c$ opposite angles A, B, and C respectively, which equation can be used to solve for the measure of angle $B$?

For a triangle with sides $a$, $b$, and $c$, and angle $C$ opposite side $c$, which equation can be used to solve for $c$ using the Law of Cosines?

Given triangle $KNM$, which of the following statements about its sides is true?

Which equation correctly uses the law of cosines to solve for $y$ in a triangle with sides $x$, $y$, $z$ and angle $C$ opposite side $y$?

In triangle $qrs$, side $r$ = $83$ cm, angle $\angle r$ = $161°$, and angle $\angle s$ = $5°$. Find the length of side $q$ to the nearest centimeter.

A rectangular sandbox has sides of length $10$ feet and $8$ feet. If the diagonal of the sandbox measures $14$ feet, which equation using the Law of Cosines can be used to find the angle between the two sides?

Given a triangle with sides $a$, $b$, and $c$, and angle $B$ opposite side $b$, which equation can be used to find the value of $b$ if side $a$ measures 8.7 cm?

Given a right triangle with legs of lengths $20$ and $21$, what is the length of the hypotenuse?

Given triangle $GHF$ inscribed in circle $c$, with points $H$ and $F$ on the circle and side lengths $GH$ = $a$, $HF$ = $b$, and $FG$ = $c$, what is the length of line segment $GH$ in terms of $b$, $c$, and the included angle $A$ opposite $GH$?

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.