사인법칙과 코사인법칙

Philadelphia is 140 miles from Washington, D.C., Washington, D.C. is 442 miles from Boston, and Boston is 315 miles from Philadelphia. Draw a triangle connecting these three cities and find the angles in the triangle.

A parallelogram has sides of length 15.4 units and 9.8 units. Its area is 72.9 square units. Find the measure of the longer diagonal.

For the following exercises, assume $\alpha$ is opposite side $a,\beta$ is opposite side $b,$ and $\gamma$ is opposite side $c.$ Solve each triangle, if possible. Round each answer to the nearest tenth.

$\beta =50^\circ ,a=105,b=45$

For the following exercises, assume $\alpha$ is opposite side $a,\beta$ is opposite side $b,$ and $\gamma$ is opposite side $c.$ Solve each triangle, if possible. Round each answer to the nearest tenth.

$\alpha =43.1^\circ ,a=184.2,b=242.8$

Solve the triangle, rounding to the nearest tenth, assuming $\alpha$ is opposite side $a,\beta$ is opposite side $b,$ and $\gamma$ is opposite side $c:\,a=4,\,b=6,c=8.$