Question

on the packaging for a triangular sail, the edge measurements for the sail are listed as 7 ft x 15 ft x 17 ft. without unfurling the sail, you want to determine if the sail forms a right triangle, an acute triangle, or an obtuse triangle. using the tools from this lesson, you determine that the general shape of the sail is a(n) triangle.

Explanation:

Step1: Recall the Pythagorean theorem and its converse

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 \(a^{2}+b^{2}\): \(a^{2}=7^{2}=49\), \(b^{2}=15^{2}=225\), so \(a^{2}+b^{2}=49 + 225=274\). Calculate \(c^{2}\): \(c^{2}=17^{2}=289\).

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

Since \(a^{2}+b^{2}=274\) and \(c^{2}=289\), and \(274<289\) (i.e., \(a^{2}+b^{2}

Answer:

obtuse triangle