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 $GH$?