Posted by **Lydia** on Thursday, July 21, 2011 at 11:18pm.

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?

- Geometry -
**Reiny**, Thursday, July 21, 2011 at 11:34pm
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.

- Geometry -
**Lydia**, Thursday, July 21, 2011 at 11:49pm
THe cosine law is confusing to me. This lesson gives no examples.

The triangle is obtuse?

- Geometry -
**Reiny**, Friday, July 22, 2011 at 8:17am
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°

- Geometry -
**Lydia**, Friday, July 22, 2011 at 1:48pm
Life saver!! = )

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