Question

the sides of a triangle have lengths 17, 48, and 49. what kind of triangle is it? acute right obtuse

Explanation:

Step1: Recall the Pythagorean - related rules

Let \(a = 17\), \(b = 48\), and \(c = 49\) (where \(c\) is the longest side). For a triangle with side - lengths \(a\), \(b\), and \(c\), 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 \(a^{2}+b^{2}\)

\[

$$\begin{align*} a^{2}+b^{2}&=17^{2}+48^{2}\\ &=289 + 2304\\ &=2593 \end{align*}$$

\]

Step3: Calculate \(c^{2}\)

\[
c^{2}=49^{2}=2401
\]

Step4: Compare \(a^{2}+b^{2}\) and \(c^{2}\)

Since \(a^{2}+b^{2}=2593\) and \(c^{2}=2401\), and \(2593>2401\), i.e., \(a^{2}+b^{2}>c^{2}\).

Answer:

acute