Question

determine the type of triangle that is drawn below.

Explanation:

Step1: Check side lengths

All side lengths \(17.43\), \(4.88\), \(5.34\) are different. So it's a scalene triangle.

Step2: Check angle type

Use the Law of Cosines \(c^{2}=a^{2}+b^{2}-2ab\cos C\). Let's assume the longest side \(a = 17.43\), \(b = 4.88\), \(c = 5.34\). Then \(\cos A=\frac{b^{2}+c^{2}-a^{2}}{2bc}=\frac{4.88^{2}+5.34^{2}-17.43^{2}}{2\times4.88\times5.34}<0\). So angle \(A\) (opposite the longest side) is obtuse.

Answer:

Scalene Obtuse