# Geometry

Tell if the measures 9,11, and 7 can be side lengths of a triangle. if so, classify the triangle as acute, right, or obtuse?

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asked by Lydia
1. Yes, the sum of any two sides is greater than the third side.

The largest angle will be opposite the 11 side.
Use the cosine law to find that largest angle.
If the cosine of that angle is negative, then that angle is obtuse.
You don't actually have to find the angle, just look at the sign of that cosine.

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posted by Reiny
2. THe cosine law is confusing to me. This lesson gives no examples.
The triangle is obtuse?

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posted by Lydia
3. let the side opposite the 11 be Ø
then ...

11^2 = 9^2 + 7^2 - 2(7)(9)cosØ
121 = 81 + 49 - 126cosØ
126cosØ = 9
cosØ = 9/126

since that is positive, Ø must be less than 90°
and since Ø is the largest angle , all angles must be acute.
So the triangle is acute angled.

Notice, it did not ask for the angles specifically, if it did, use your calculator to find
cos^-1 (9/126) to get Ø = 85.9°

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posted by Reiny
4. Life saver!! = )

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posted by Lydia

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