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) $\boldsymbol{square}$ triangle.

Explanation:

Step1: Identify sides and square them

Let \(a=7\), \(b=15\), \(c=17\) (longest side).
Calculate squares: \(a^2 = 7^2 = 49\), \(b^2 = 15^2 = 225\), \(c^2 = 17^2 = 289\)

Step2: Sum squares of shorter sides

Sum \(a^2 + b^2 = 49 + 225 = 274\)

Step3: Compare to square of longest side

Compare \(274\) and \(289\): \(a^2 + b^2 < c^2\)

Answer:

obtuse