Question

the sides of a triangle are shown. determine if the triangle is an acute, right or obtuse triangle. 15, 20, 30

Explanation:

Step1: Recall the triangle - type rules

Let \(a = 15\), \(b = 20\), \(c = 30\) (where \(c\) is the longest side). For a triangle with side lengths \(a\), \(b\), and \(c\) (\(c\) being the longest side), if \(a^{2}+b^{2}=c^{2}\), it is a right - triangle; if \(a^{2}+b^{2}>c^{2}\), it is an acute - triangle; if \(a^{2}+b^{2}

Step2: Calculate \(a^{2}+b^{2}\) and \(c^{2}\)

Calculate \(a^{2}=15^{2}=225\), \(b^{2}=20^{2}=400\), so \(a^{2}+b^{2}=225 + 400=625\). Calculate \(c^{2}=30^{2}=900\).

Step3: Compare \(a^{2}+b^{2}\) and \(c^{2}\)

Since \(625<900\), that is \(a^{2}+b^{2}

Answer:

The triangle is an obtuse triangle.