Geometry multiple choice question can anybody help me??

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1 Answer
Dean R.
May 11, 2018

Obtuse and # { 13 sqrt{2} }/2#

Explanation:

  1. Triangle #a=16, b=30, c=38,# acute, obtuse or right?

The biggest angle is opposite the biggest side. Let's calculate its cosine using the Law of Cosines.

#c^2 = a^2 + b^2 - 2 a b cos C#

#cos C = {a^2 + b^2 - c^2}/{2ab} = {16^2+30^2+38^2}/{2(30)(38)} = -12/95#

It's negative, so #C>90^circ#, an obtuse triangle. The sign was determined by the numerator, interestingly turning the Pythagorean Theorem into a triangle classifier.

  1. In 45/45/90 triangle, the second biggest cliche in trig, the legs are equal:

# x^2 + x^2 = 13^2 #

#2x^2 = 13^2 #

# x = 13/sqrt{2} = 13/2 sqrt{2}#
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