Geometry Law of Sines and Law of Cosines Quiz: 10 Questions with Explanations

A 22B 44C 88D 38

Area = 1/2 x 8 x 11 x sin 30 = 22. Forgetting the 1/2 gives 44 (with sin 30 = 0.5).

A b / cos BB sin B / bC b / sin BD b x sin B

Each side over the sine of its opposite angle gives the same ratio.

A Law of SinesB Law of CosinesC Pythagorean theorem onlyD Area formula only

SAS gives the third side with the Law of Cosines.

A 67B 130C 193D 16

c squared = 49 + 81 – 2(7)(9)(0.5) = 67. The value 130 forgets the cosine term.

A 5B 10C 20D 17.3

b / sin 90 = 10 / sin 30, so b = 10 / 0.5 = 20.

A 60 degreesB 90 degreesC 45 degreesD 120 degrees

cos C = (9 + 16 – 25)/24 = 0, so C is 90 degrees.

A Find the third angle, 65 degrees, and use the Law of SinesB Use the Law of Cosines with 10 and 40C Add the angles to get 115D Use the Pythagorean theorem

AAS: first find the third angle (180 – 115 = 65), then use the Law of Sines.

A 5B 7C All are equalD 9

The longest side is opposite the largest angle.

A It gives a negative lengthB It becomes the Pythagorean theoremC It becomes the Law of SinesD It gives 180 degrees

cos 90 = 0, so the last term vanishes and c squared = a squared + b squared.

A 18B 9C 31.2D 15.6

(1/2)(36)(0.866) = 15.6. Using sin 60 = 1 gives 18.