5.8 Non-right triangles: law of cosines  (Page 5/8)

Explain the relationship between the Pythagorean Theorem and the Law of Cosines.

When must you use the Law of Cosines instead of the Pythagorean Theorem?

$\gamma =\mathrm{41.2°},a=2.49,b=3.13$

$\alpha =\mathrm{120°},b=6,c=7$

$\beta =\mathrm{58.7°},a=10.6,c=15.7$

$\gamma =\mathrm{115°},a=18,b=23$

$\alpha =\mathrm{119°},a=26,b=14$

$\gamma =\mathrm{113°},b=10,c=32$

$\beta =\mathrm{67°},a=49,b=38$

$\alpha =\mathrm{43.1°},a=184.2,b=242.8$

$\alpha =\mathrm{36.6°},a=186.2,b=242.2$

$\beta =\mathrm{50°},a=105,b=45{}_{}{}^{}$

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

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

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

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

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

$A=\mathrm{35°},b=8,c=11$

$B=\mathrm{88°},a=4.4,c=5.2$

$C=\mathrm{121°},a=21,b=37$

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

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

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

Find the area of a triangle with sides of length 18 in, 21 in, and 32 in. Round to the nearest tenth.

Find the area of a triangle with sides of length 20 cm, 26 cm, and 37 cm. Round to the nearest tenth.

$a=\frac{1}{2}\text{m},b=\frac{1}{3}\text{m},c=\frac{1}{4}\text{m}$

$a=12.4\text{ ft},b=13.7\text{ ft},c=20.2\text{ ft}$

$a=1.6\text{ yd},b=2.6\text{ yd},c=4.1\text{ yd}$

Find the measure of each angle in the triangle shown in [link] . Round to the nearest tenth.

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 11 feet and 17 feet. The longer diagonal is 22 feet. Find the length of the shorter 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.

A regular octagon is inscribed in a circle with a radius of 8 inches. (See [link] .) Find the perimeter of the octagon.

A regular pentagon is inscribed in a circle of radius 12 cm. (See [link] .) Find the perimeter of the pentagon. Round to the nearest tenth of a centimeter.

Draw the triangle.

Find the length of the third side.