Answer:
B) Acute
Explanation:
You want to classify a triangle with side lengths 21 km, 25 km, and 29 km.
Form factor
A "form factor" for the triangle can be calculated from its side lengths as ...
f = a² +b² -c² . . . . . where c is the longest side
Here, that value is ...
f = 21² +25² -29² = 225
The interpretation is as follows:
- f > 0 — acute
- f = 0 — right
- f < 0 — obtuse
The given triangle is an acute triangle.
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Additional comment
This comes from the Law of Cosines. The largest angle in the triangle is ...
arccos(f/(2ab)) = arccos(225/(2·21·25)) = arccos(3/14) ≈ 77.6°
The signs of 'a' and 'b' are positive, so the sign of the cosine matches the sign of 'f'. This makes 'f' a handy classifier of triangles.