Asked by Lydia
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?
Answers
Answered by
Reiny
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.
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.
Answered by
Lydia
THe cosine law is confusing to me. This lesson gives no examples.
The triangle is obtuse?
The triangle is obtuse?
Answered by
Reiny
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°
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°
Answered by
Lydia
Life saver!! = )
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