1. Grade 10 Academic (MPM2D) Unit 6: Trigonometry 2: Non-Right Triangles SSA - Triangles Investigations
Mr. Choi
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2. Trigonometry is a branch of mathematics that studies the relationship between the measures of the angles and the lengths of the sides in triangles.
SSA Triangles Investigations
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3. Notation: In any triangle, the vertices are named using capital letters as in the given example. The lengths of the sides are named using lower case letters that match the opposite vertex.
SSA Triangles Investigations
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4. Sine (Sin), COSINE (Cos), TANGENT (Tan):
Opposite side
Adjacent side
Hypotenuse side
SSA Triangles Investigations
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5. Sine Law Cosine Law a Using Cosine Law to find the angles or
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SSA Triangles Investigations

6. Steps to solve triangle
Right triangles can be solved with the primary trig. Ratios
Non-rights triangles can be solved with sine law & cosine law.
Use Sine Law if: - 2 sides and one opposite angle to one of the given sides are known (SSA) - 2 angles and one opposite side to one of the given angles are known (AAS)
Use Cosine Law if: - all 3 sides are known (SSS) - 2 sides and a contained angle are known (SAS)
Applications of Sine & Cosine Laws
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7. SINE Law (Alternate possibilities
SINE Law (Alternate possibilities!!) Sine Law can be used to compute the remaining sides of a triangle when two angles and a side are known. It can also be used when two sides and one of the non-enclosed angles are known. In some such cases, the triangle is not uniquely determined by this data (called the ambiguous case) and the technique gives two possible values for the enclosed angle. You are going to learn in more detail in the next course.
SSA Triangles Investigations
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8. SSA: when the given angle B is acute
Given where point A is on the horizontal, line and a line segment AC.
3 cm is the required length to form a right triangle.
SSA Triangles Investigations
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9. SSA: when the given angle is acute
Given Side
3rd Side
Given Angle
Recommendation:
In SSA situation, built the triangle from the horizontal.
Start with the Given Angle from the horizontal line.
Attach the Given Angle with the Given side,
Attach the Given side, with the 3rd side accordingly as shown in the picture above.
SSA Triangles Investigations
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10. SSA: when the given angle B is acute
Given where point A is on the horizontal, line and a line segment AC.
Given side (6cm)
Given angle: 30o
Case 1: If AC = 3 cm
Start the angle from horizontal line!!
3 cm A
Therefore:
1 right triangle can be formed.
Given side (6cm) x sin(given angle)
= 3rd Side (3 cm)
SSA Triangles Investigations
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11. SSA: when the given angle B is acute
Given where point A is on the horizontal, line and a line segment AC.
Given side (6cm)
Given angle: 30o
Case 2: If AC < 3 cm
Start the angle from horizontal line!!
2 cm A
ie: Let AC = 2 cm
Given side (6cm) x sin(given angle)
Therefore:
No triangle can be formed.
> 3rd Side (2 cm)
SSA Triangles Investigations
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12. SSA: when the given angle B is acute
Given where point A is on the horizontal, line and a line segment AC.
Given side (6cm)
Given angle: 30o
Case 3: If 3cm < AC < 6 cm
Start the angle from horizontal line!!
4 cm A’
4 cm A
ie: Let AC = 4 cm
Given side (6cm) x sin(given angle)
Therefore:
Two triangles can be formed.
< 3rd Side (4 cm) < Given Side (6cm)
SSA Triangles Investigations
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13. SSA: when the given angle B is acute
Given where point A is on the horizontal, line and a line segment AC.
Given side (6cm)
Given angle: 30o
Case 4: If AC = 6 cm
Start the angle from horizontal line!!
6 cm A
ie: Let AC = 6 cm
Therefore:
1 Isosceles triangle can be formed.
Given side (6cm) = 3rd Side (6cm)
SSA Triangles Investigations
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14. SSA: when the given angle B is acute
Given where point A is on the horizontal, line and a line segment AC.
Given side (6cm)
Given angle: 30o
Case 5: If AC > 6 cm
Start the angle from horizontal line!!
8 cm A
ie: Let AC = 8 cm
Therefore:
1 obtuse triangle can be formed.
Given side (6cm) < 3rd Side (8cm)
SSA Triangles Investigations
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15. Example 1: In , d = 64cm, f = 42 cm, and. Solve the triangle
Example 1: In , d = 64cm, f = 42 cm, and Solve the triangle. Round to nearest degrees and nearest tenth - centimeters.
Triangle 1
Supplementary Angles
84°
42 cm D
61°
72.8 cm
Given side (64cm) x sin(given angle)
Two triangles can be formed.
< 3rd Side (42 cm) < Given Side (64cm)
SSA Triangles Investigations
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16. Example 1: Continued In , d = 64cm, f = 42 cm, and. Solve the triangle
Example 1: Continued In , d = 64cm, f = 42 cm, and Solve the triangle. Round to nearest degrees and nearest tenth - centimeters.
Triangle 2
42 cm D’
26°
119°
32.1cm
Supplementary Angles
Given side (64cm) x sin(given angle)
Two triangles can be formed.
< 3rd Side (42 cm) < Given Side (64cm)
SSA Triangles Investigations
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17. SSA: when the given angle is acute (Summary)
Given Side
3rd Side
Given Angle
Given Side x sin(Given Angle) = 3rd Side
 1 Right Triangle
Given Side x sin(Given Angle) > 3rd Side
 No Triangle
Given Side x sin(Given Angle) < 3rd Side < Given Side
 2 Triangles
Given Side = 3rd Side
 1 Isosceles Triangle
Given Side < 3rd Side
 1 Obtuse Triangle
SSA Triangles Investigations
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18. What if the given angle B is an obtuse angle??
3rd Side
Given Side
Given Angle (obtuse)
A triangle can be formed only when….
3rd Side > Given Side
Will be discussed in next course!
SSA Triangles Investigations
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19. Homework
Work sheet: SSA – Investigations Exercise: #1-4 Text: Check the website for updates
SSA Triangles Investigations
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20. End of lesson Applications of Sine & Cosine Laws
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