Test #1



Math 240 Ch 7 Review

Instructor: Butler

1. Oblique Triangle a triangle that is not a ______________ triangle.

2. Solving a Triangle The measure of the three sides and the three angles of a triangle can be found if at least ________________ and any other two measures are known.

4 possible cases:

case 1: SAA or ASA Use Law of ______________

case 2: SSA (angle not between the sides) Use Law of _______________

may lead to more than one triangle.

case 3: SAS (angle between the sides) Use Law of ________________

case 4: SSS Use Law of _________________

Step by step procedures to solve the triangle:

case 1: SAA or ASA

Step 1 Find the remaining angle using the angle sum formula (A + B + C = 180°)

Step 2 Find the remaining two sides using the Law of Sines.

Example 1) Solve the right triangle ABC given B = 52°, C = 29°, and a = 43cm

case 2: SSA

Step 1 Find an angle using the Law of Sines.

Step 2 Find the remaining angle using the angle sum formula.

Step 3 Find the remaining side using the Law of Sines

(there may be no triangle, one triangle, or two triangles that exist)

Example 2) Solve the right triangle ABC given A = 61.7°, a = 78.9m, and b = 86.4m

case 3: SAS

Step 1 Find the 3rd side using the Law of Cosines.

Step 2 Find the smaller of the 2 remaining angles using the Law of Sines.

Step 3 Find the remaining angle using the angle sum formula.

Example 3) Solve the right triangle given A = 121°, b = 5cm, c = 3cm

case 4: SSS

Step 1 Find the largest angle using the Law of Cosines.

Step 2 Find either remaining angle using the Law of Sines.

Step 3 Find the remaining angle using the angle sum formula.

Example 4) Solve the right triangle given a = 9.3 in., b = 5.7 in., c = 8.2 in.

3. Area of a Triangle for any ∆ABC

First method

Use this method if you know the measures of SAS

[pic] [pic] [pic]

Example 5) Find the area of the triangle ABC given C = 72.2°, b = 43.8m, a = 35.1m

Second method

Use this method if you know the measures of SSS

Heron’s Area Formula in a ∆ABC with lengths a,b,c

[pic]

where [pic] is the semi perimeter [pic]

Example 6) Find the area of the triangle ABC given a = 43ft., b = 32ft., c = 51ft.

Answers____________________________________________________________________

1. right 2. one side Case 1) Sines Case 2) Sines Case 3) Cosines Case 4) Cosines

Example 1) A=99°, b=34cm, c=21cm

Example 2) B1=74.6°, C1=43.7°, c1=61.9m, B2=105.4°, C2=12.9°, c2=20.0m

Example 3) a=7cm, B=37.6°, C=21.4°

Example 4) A=82°, B=37°, C=61°

Example 5) 732 m² Example 6) 680ft²

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