If none of the angles of a triangle is a right angle, the triangle is called oblique. All angles are acute Two acute angles, one obtuse angle

To solve an oblique triangle means to find the lengths of its sides and the measurements of its angles.

FOUR CASES CASE 1: One side and two angles are known (SAA or ASA). CASE 2: Two sides and the angle opposite one of them are known (SSA). CASE 3: Two sides and the included angle are known (SAS). CASE 4: Three sides are known (SSS).

CASE 1: ASA or SAA S A A ASA S AA SAA

S S A CASE 2: SSA

S S A CASE 3: SAS

S S S CASE 4: SSS

The Law of Sines is used to solve triangles in which Case 1 or 2 holds. That is, the Law of Sines is used to solve SAA, ASA or SSA triangles.

Law of Sines

For a triangle with sides a, b, and c, and angles A, B, and C

5 b c

12 a b

The area A of a triangle is where b is the base and h is the altitude drawn to that base.

h b a

The area A of a triangle equals one-half the product of two of its sides times the sine of its included angle.

Find the area of a triangle ABC if a = 5, C = 65 degrees, and B = 45 degrees.

No triangle with the given measurements! 3 5 a

5 3 a

Two triangles!!

Triangle 1:

Triangle 2:

Lesson Overview 5-6B

5-Minute Check Lesson 5-7A

Lesson Overview 5-7A

Lesson Overview 5-7B

5-Minute Check Lesson 5-8A

Heron’s Formula The area A of a triangle with sides a, b, and c is

Lesson Overview 5-6A