2.3 Part 2 Properties of Triangles
Warm-up:
Find angle A
2.3b Properties of Triangles
Determine the height of each of the following SSA (not a contained angle) triangles.
In general, the height of a triangle can be determined by using SOH CAH TOA
h = bsinA
Investigation:
Given Acute Angle A
1. What happens if side 'a' is less than the height?
2. What happens is side 'a' is the same as the height?
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2. What happens is side 'a' is the same as the height?
3. What happens if side 'a' is longer than the height?
In summary, given an SSA triangle, for an acute angle A.
1. If a < h, then no triangle exists
2. If a = h, then one triangle exists (It is a right triangle)
3. If a > h then we have to compare 'a' to 'b'
- if a ≥ b, then one triangle exists. (Too long to swing!)
-if h < a < b, then two triangles exist. This is the ambiguous case
Given Obtuse Angle A
1. side a is less than side b
2. side a = side b
3. side a > side b
In summary, given a SSA triangle, for an
obtuse angle A:
1. If a ≤ b, then no triangle exists
2. If a > b then one triangle exists
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Example. Determine the number of solutions for the following triangles.
p109 #11
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