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 triangle classification rule

For a triangle with side lengths $a \leq b \leq c$, use:

• $a^2 + b^2 = c^2$: right triangle
• $a^2 + b^2 > c^2$: acute triangle
• $a^2 + b^2 < c^2$: obtuse triangle

Step2: Assign sides and compute squares

Let $a=7$, $b=15$, $c=17$.
$a^2 = 7^2 = 49$, $b^2 = 15^2 = 225$, $c^2 = 17^2 = 289$

Step3: Sum smaller squares, compare to largest

Sum: $49 + 225 = 274$
Compare: $274 < 289$

Answer:

obtuse