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?
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 cosine law is confusing to me. This lesson gives no examples.
The triangle is obtuse?
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°
Life saver!! = )
To determine if the measures 9, 11, and 7 can be side lengths of a triangle, we need to use the triangle inequality theorem. According to this theorem, in any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
In this case, let's compare the lengths:
9 + 11 = 20
11 + 7 = 18
7 + 9 = 16
From these calculations, we can see that the sum of the lengths of the two smaller sides must be greater than the length of the longest side. However, the sum of 9 and 7 is 16, which is equal to the length of the longest side (11).
Since the sum of the two smaller sides is not greater than the length of the longest side, these lengths cannot form a triangle.
Therefore, it is not possible to classify this triangle as acute, right, or obtuse since it does not exist.