Section 14 - 4: Area and The Law of Sines

Section 14 - 4: Area and The Law of Sines

To find different unknowns in oblique triangles.

Some definitions

• Oblique Triangle: A triangle that does not have a right angle.

• Height (Of an oblique triangle): the length of an altitude.

• Altitude: A segment with one endpoint at a vertex that is perpendicular to the line containing the opposite side (the base of the triangle.)

• Area of a Triangle: one - half the product of the base and the height.

Formula for AREA of Oblique Triangle

• Area = (a*c*sinB)/2 or (b*c*sinA)/2 or (a*b*sinC)/2

• Why it works...

• Area = (h*a)/2

• sinB=h/c so h = c*sinB replace h in area formula.

• sinC = h/b so h = b*sinC replace h in area formula.

An example

• Formula for area: (side 1)(side 2)(sin(included angle))/2

• (12*(8.2)*sin114)/2

• =44.95 square units

Multiple Choice

Find the Area of the Triangle.

• 13.9 in²

• 28 in²

• 56 in²

• 32 in²

Multiple Choice

Find the Area of the Triangle.

• 11.9 yd²

• 24 yd²

• 48 yd²

• 23.8 yd²

Multiple Choice

Find the Area of the Triangle.

• 48 cm²

• 24 cm²

• 32.2 cm²

• 62.1 cm²

Law of Sines

• Let's look at that same triangle and think about the height.

• sinB=h/c so h = c*sinB replace h in area formula.

• sinC = h/b so h = b*sinC replace h in area formula.

• If they both equal "h" then they must equal each other.

• c*sinB=b*sinC

• SO...b/sinB = c/sinC

Multiple Choice

Find AB

• 10
• 8
• 6.1
• 4.9

Multiple Choice

Use the Law of Sines to solve for BC

• 33
• 24
• 12
• 29

Please change 19 m for side BC to 21 meters! Thanks!

Multiple Choice

What is the measure of angle A?

• 58 degrees
• 61 degrees
• 78 degrees
• 74 degrees

Multiple Choice

Find BC

• A
• B
• C
• D

Multiple Choice

Find the area of ABC to the nearest tenth.

• 62.3 units²

• 124.6 units²

• 77.0 units²

• 100 units²

Multiple Choice

Find m<B

• A

• B

• C

• D