Triangle angle

Geometry Level 2

John, Felix and Simon are arguing about a triangle. The side lengths of the triangle are 5, 12 and 15. John thinks that the triangle is acute, while Felix thinks it is right and Simon thinks it is obtuse. Who is correct among the three?

John Felix Simon

1 solution

A Former Brilliant Member
Mar 16, 2018

Apply cosine rule to know the angles of each vertex.

$15^2=5^2+12^2-2(5)(12)(\cos A)$ $\implies$ $A \approx 117.818$

$12^2=5^2+15^2-2(5)(15)(\cos C)$ $\implies$ $C \approx 45.036$

$5^2=12^2+15^2-2(12)(15)(\cos B)$ $\implies$ $B \approx 17.146$

There is an angle greater than 90 degrees, so it is an obtuse triangle. Simon is correct.

Triangle angle

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