Chapter 6

Trigonometry- Part 3

Aim #6.1:How do we apply the Law of Sines?

An oblique triangle is one that does not contain a right angle.

Law of Sines states… If A, B, and C are the measures of the angles of a

triangle and a, b, and c are the lengths of the sides opposite these angles, then

The ratio of the length of the side of any triangle to the sine of the angle opposite that side is the same for all three sides of the triangle.

CSin

c

BSin

b

ASin

a

Example 1: Using the Law of Sines for an SAA triangle

Solve the triangle below with A= 46º, C=63º, and c = 56 inches.

Round the lengths of the sides to the nearest tenth.

Check for Understanding:

Solve the triangle below with A= 64º, C=82º, and c = 14 centimeters.

Round the lengths of the sides to the nearest tenth.

Example 2: Using the Law of Sines for an ASA triangle

Solve the triangle below with A= 50º, C=33.5º, and b = 76.

Round your measures to the nearest tenth.

Check for Understanding:

Solve triangle ABC if A= 40º, C=22.5º, and b = 12.

Round your measures to the nearest tenth.

Example 3: Solving SAA Triangle

Solve triangle ABC, if A= 43°, a = 81 and b = 62.

Round lengths to the nearest tenth and angle measures to nearest degree.

Check for Understanding:

Solve triangle ABC if A= 57°, a = 33, and b = 26.

Round lengths to the nearest tenth and angle measures to nearest degree.

Example 4: Solving SSA Triangle

Solve triangle ABC if A= 75°, a = 51 and b = 71.

Check for Understanding:

Solve triangle ABC if A= 50°, a = 10 and b =20.

Example 5: Solving an SSA Triangle

Check for Understanding:

Solve triangle ABC if A = 35°, a = 12 and b = 16.

Round lengths to the nearest tenth and angle measures to nearest degree.

The Area of an Oblique Triangle:

Example 6: Finding the Area

Find the area of a triangle having two sides of lengths 24 meters and 10 meters and an included angle of 62°.

Round to the nearest square meter.

Check for Understanding:

Find the area of a triangle having two sides of lengths 8 meters and 12 meters and an included angle of 135°.

Round to the nearest square meter.

Summary: Answer in complete sentences.