사인법칙과 코사인법칙

For the following exercises, assume $\alpha$ is opposite side $a,\beta$ is opposite side $b,$ and $\gamma$ is opposite side $c.$ If possible, solve each triangle for the unknown side. Round to the nearest tenth.

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

For the following exercises, assume $\alpha$ is opposite side $a,\beta$ is opposite side $b,$ and $\gamma$ is opposite side $c.$ If possible, solve each triangle for the unknown side. Round to the nearest tenth.

$\alpha =36.6^\circ ,a=186.2,b=242.2$

For the following exercises, assume $\alpha$ is opposite side $a,\beta$ is opposite side $b,$ and $\gamma$ is opposite side $c.$ If possible, solve each triangle for the unknown side. Round to the nearest tenth.

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

For the following exercises, use the Law of Cosines to solve for the missing angle of the oblique triangle. Round to the nearest tenth.

$a=42,b=19,c=30;$ find angle $A.$

For the following exercises, use the Law of Cosines to solve for the missing angle of the oblique triangle. Round to the nearest tenth.

$a=14,\,b=13,\,c=20;$ find angle $C.$

For the following exercises, use the Law of Cosines to solve for the missing angle of the oblique triangle. Round to the nearest tenth.

$a=16,b=31,c=20;$ find angle $B.$

For the following exercises, use the Law of Cosines to solve for the missing angle of the oblique triangle. Round to the nearest tenth.

$a=13,\,b=22,\,c=28;$ find angle $A.$

For the following exercises, use the Law of Cosines to solve for the missing angle of the oblique triangle. Round to the nearest tenth.

$a=108,\,b=132,\,c=160;$ find angle $C.$

For the following exercises, solve the triangle. Round to the nearest tenth.

$A=35^\circ ,b=8,c=11$

For the following exercises, solve the triangle. Round to the nearest tenth.

$B=88^\circ ,a=4.4,c=5.2$

For the following exercises, solve the triangle. Round to the nearest tenth.

$C=121^\circ ,a=21,b=37$

For the following exercises, solve the triangle. Round to the nearest tenth.

$a=13,b=11,c=15$

For the following exercises, solve the triangle. Round to the nearest tenth.

$a=3.1,b=3.5,c=5$

For the following exercises, solve the triangle. Round to the nearest tenth.

$a=51,b=25,c=29$

A parallelogram has sides of length 16 units and 10 units. The shorter diagonal is 12 units. Find the measure of the longer diagonal.

The sides of a parallelogram are 28 centimeters and 40 centimeters. The measure of the larger angle is 100°. Find the length of the shorter diagonal.

For the following exercises, suppose that ${x}^{2}=25+36-60\cos (52)$ represents the relationship of three sides of a triangle and the cosine of an angle.

Draw the triangle.

For the following exercises, suppose that ${x}^{2}=25+36-60\cos (52)$ represents the relationship of three sides of a triangle and the cosine of an angle.

Find the length of the third side.

An airplane flies 220 miles with a heading of 40°, and then flies 180 miles with a heading of 170°. How far is the plane from its starting point, and at what heading? Round answers to the nearest tenth.

Los Angeles is 1,744 miles from Chicago, Chicago is 714 miles from New York, and New York is 2,451 miles from Los Angeles. Draw a triangle connecting these three cities, and find the angles in the triangle.