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**SOLVING FOR THE MISSING PART OF AN OBLIQUE TRIANGLE**

LAW OF SINES SOLVING FOR THE MISSING PART OF AN OBLIQUE TRIANGLE

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**An oblique triangle is a triangle that has no right angles.**

C B A a b c To solve an oblique triangle, you need to know the measure of at least one side and the measures of any other two parts of the triangle – two sides, two angles, or one angle and one side.

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**The following cases are considered when solving oblique triangles.**

Two angles and any side (AAS or ASA) 2. Two sides and an angle opposite one of them (SSA) C c a a c b 3. Three sides (SSS) 3 c a B 4. Two sides and their included angle (SAS)

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**If ABC is an oblique triangle with sides a, b, and c, then**

The first two cases can be solved using the Law of Sines. (The last two cases can be solved using the Law of Cosines.) Law of Sines If ABC is an oblique triangle with sides a, b, and c, then C B A b h c a C B A b h c a Acute Triangle Obtuse Triangle

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The Law of Sines Use when the given info is… ASA or AAS.

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**The Law of Sines Start by solving Solve ∆ABC if A = 42º,**

for the missing angle. Solve ∆ABC if A = 42º, b = 6.4, and C = 81º. B = 180º - 42º - 81º B = 57º

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**The Law of Sines Solve ∆ABC if A = 42º, b = 6.4, and C = 81º.**

Then solve for one of the missing sides.

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**The Law of Sines Solve ∆ABC if A = 42º, b = 6.4, and C = 81º.**

Finally solve for the remaining side.

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**Example (SSA): Use the Law of Sines to solve the triangle.**

A = 110°, a = 125 inches, b = 100 inches C B A b = 100 in c a = 125 in 110° 21.26° 48.74° 48.23 in C ≈ 180° – 110° – 48.74° = 21.26°

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**Use the Law of Sines to find side b and c.**

Example (ASA): Find the remaining angle and sides of the triangle. C B A b c 60° 10° a = 4.5 ft The third angle in the triangle is A = 180° – A – B = 180° – 10° – 60° = 110°. 4.15 ft 110° 0.83 ft Use the Law of Sines to find side b and c.

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**Now, you try some! Solve these triangles. A = 40° B = 20° a = 2**

Always draw your triangle before you use the Sine Law Now, you try some! Solve these triangles. A = 40° B = 20° a = 2 A = 110° C = 30° c = 3 3) A = 30° b = C = 50° 4) c = 2 A = 40° B = 40°

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LAW OF SINES: THE AMBIGUOUS CASE. MENTAL DRILL Identify if the given oblique triangle can be solved using the Law of Sines or the Law of Cosines 1. X.

LAW OF SINES: THE AMBIGUOUS CASE. MENTAL DRILL Identify if the given oblique triangle can be solved using the Law of Sines or the Law of Cosines 1. X.

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