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2 years ago

PLEASE HELP ILL MAKE YOU BRAINIEST

Mathematics

1 answer:

katovenus [111]2 years ago

3 0

Answer:

obtuse

Step-by-step explanation:

A "form factor" can be computed whose sign will tell you the classification of the triangle. For short sides a, b and long side c, the form factor is ...

f = a² +b² -c²

And the interpretation is ...

f > 0 . . . acute
f = 0 . . . right
f < 0 . . . obtuse

<h3>form factor</h3>

For the given side lengths, the form factor is ...

f = 11² +15² -20² = 121 +225 -400

f = -54

<h3>interpretation</h3>

The value is less than zero, signifying an obtuse triangle.

_____

<em>Additional comment</em>

The value f/(2ab) = -54/(2·11·15) = -9/55 is the cosine of the largest angle. Here, the largest angle is arccos(-9/55) ≈ 99.4°. This is greater than 90°, hence an obtuse angle.

This cosine relation comes from the Law of Cosines. The interpretation of the "form factor" can be developed by considering the Pythagorean theorem (f=0 ⇒ right triangle) and the relationship between sides and angles. If the longest side is longer than necessary for a right triangle, the largest angle will be greater than 90°.

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