Right Triangle vs Oblique Triangle

Sine

100

An oblique triangle has two angles and the non-included side given, can you apply the law of sine?

Yes

200

Find the missing angle B of the triangle where A = 49, side a is 12, and b = 15. Write your answer in the nearest tenths.

70.6 degrees

300

If a = 12, B = 27 degrees, and b = 15, find A to the nearest degree using the Law of Sines. Round to the nearest whole number.

21 degrees

400

If A = 50 degrees, b = 10, and a = 14, find C to the nearest degree using the Law of Sines. Round to the nearest whole number.

97 degrees

500

If A = 123.9 degrees, B = 22.2 degrees, and b = 27.5, find c to the nearest tenth using the Law of Sines. Round to the nearest tenths.

40.6 units

Cosine

100

An oblique triangle has three angles given, can you apply the law of cosine?

No

200

 This method will allow you to solve for triangles where you have either SAS or SSS.

Cosine Law

300

If a = 3, b = 7 and c = 5, find B to the nearest degree using the Law of Cosines.

120 degrees

400

If a = 5, b = 6, and c = 8, find A to the nearest degree using the Law of Cosines.

39 degrees

500

If a = 12.6, b = 8.5, and c = 6.3, find C to the nearest tenths using the Law of Cosines.

26.7 degrees

Mixed

100

Given an oblique triangle, find the missing angle C. If  A = 33 and B = 47

100 degrees

200

Find the missing angle of the right triangle if one of the angles is equal to 49 degrees.

41 degrees

300

Lara's radar on her submarine detects two other subs nearby. The first sub is 360m away, the second sub is 250m, and the angle between them is 34.34 degrees. What is the distance between the other two subs?

302.40m

400

A soccer player takes a shot on a standard net that is 7.3m wide. If the player is 10m from one goalpost and 14m from the other, through what angle can a goal be made?

29.9 or 30 degrees

500

Scientists in Houston are trying to figure out the distance from a satellite to Cape Canaveral. They know that the satellite is 530 miles from Houston at an 85º angle of elevation, and Houston and Cape Canaveral, in a straight line from one to the other, are 902 miles apart. How far is the satellite from Cape Canaveral?

1005.57 miles

Right Triangle Trig

100

The ratio of the adjacent side to the hypotenuse?

cosine

200

What is the measurement of the angle opposite to the longest side of a right triangle?

90 degrees

300

Find sin A, if a = 22, and c = 34. Round to the nearest tenths.

0.6

400

Find tan A, if sin A = 3/7, and cos A = 4/7. Write the exact value.

0.75

500

Find cot A, if csc A = 25/16, and sec A = 25/19. Round to the nearest tenths.

1.2

Proving Trig Identities

100

What is the reciprocal identity of csc x?

1/sin x

200

(sin²x+cos²x)¹⁰⁰

1

300

Simplify: (csc y)(tan y)

sec y

400

Simplify: (sin²x+cos²x)/sin x - cos x cot x

sin x

500

(tan²x) (csc²x) + (sec²x) (1 - sin²x)

sec²x