Laws of Sines, Law of Cosines, and Area

Sine

100

If A = 63 degrees, B = 19 degrees, and a = 2.4, find b to the neareast hundredth.

0.88 units

200

If B = 14 degrees, C = 45 degrees, and b = 5.2, find c to the nearest hundredth.

15.2 units

300

If a = 12, B = 27 degrees, and b = 15, find A to the nearest degree.

21 degrees

400

If A = 50 degrees, b = 10, and a = 14, find C to the nearest degree.

97 degrees

500

If A = 123.9 degrees, B = 22.2 degrees, and b = 27.5, find c to the nearest hundredth.

40.59 units

Cosine

100

If a = 21.5, b = 13, and C = 39 degrees, find c to the nearest hundredth.

14.03 units

200

If A = 52 degrees, b = 54 and c = 49, find a to the nearest hundredth.

45.38 units

300

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

120 degrees

400

If a = 5, b = 6, and c = 8, find A to the nearest hundredth.

38.62 degree

500

If a = 12.6, b = 8.5, and c = 6.3, find C to the nearest hundredth.

26.7 degree

Application

100

In order to solve the triangle given b = 40, c = 45, and A = 51, which law should you use first to solve.

Cosine Law

200

What combination of sides and angles requires you to check for a possible second solution?

Angle - Side - Side

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 degree. What is the distance between the other two subs?

208.50m

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?

29.91 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

Area

100

Find the area of triangle ABC if B=25 degrees, a =17m and c=33m to the nearest hundredth.

118.54 m²

200

Find the area of triangle ABC if A=32, b=10cm and c=12cm to the nearest hundreth.

31.8 cm²

300

Find the area of triangle ABC if <C=90, b=20mm and c=25mm to the nearest hundredth.

150 mm²

400

Find the area of triangle ABC if a=3 km, b=19 km and c= 21 km.

22.30 km²

500

Find the area of triangle ABC if A=36, B = 31.97 and c=7cm to the nearest hundredth.

8.2 cm²