Answer: A) 0 triangles
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Explanation:
Adding up the two smaller sides gets us 9.6+11.6 = 21.2, but this result is not larger than the third side of 21.2
For a triangle to be possible, we need to be able to add any two sides and have the sum be larger than the third remaining side. This is the triangle inequality theorem.
I recommend you cutting out slips of paper with these side lengths and trying it out yourself. You'll find that a triangle cannot be formed. The 9.6 cm and the 11.6 cm sides will combine to form a straight line that is 21.2 cm, but a triangle won't form.
As another example of a triangle that can't be formed is a triangle with sides of 3 cm, 5 cm, and 8 cm. The 3 and 5 cm sides add to 3+5 = 8 cm, but this does not exceed the third side. The best we can do is form a straight line but that's not a triangle.
In short, zero triangles can be formed with the given side lengths of 9.6 cm, 11.6 cm, and 21.2 cm
For #1 the answers are
69 degrees
155 degrees
86 degrees
335 degrees
249 degrees
Answer is -10
Work: -(5+5)
In triangle, ABD,
AD²= AB²+BD²
AB² = AD²-BD²
AB² = 18²-9² = 324-81 = 243
AB = √243
In triangle, ABC,
AC² = AB²+BC²
AC² = (√243)²+(13)²
AC² = 243+169
AC = √412
AC = 20.29
