Question

on the packaging for a triangular sail, the edge measurements for the sail are listed as 7 ft × 15 ft × 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 triangle inequality and the Pythagorean theorem for triangle type determination.

For a triangle with side lengths \(a\), \(b\), and \(c\) (where \(c\) is the longest side), we use the following:

• 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}

Here, the side lengths are \(7\) ft, \(15\) ft, and \(17\) ft. The longest side \(c = 17\) ft, \(a = 7\) ft, \(b = 15\) ft.

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

Answer:

obtuse