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 Inequality Test

For a triangle with side lengths \(a\), \(b\), \(c\) (where \(c\) is the longest side), we use the Pythagorean theorem and its extensions. The formula to check the type of triangle is:

• If \(a^2 + b^2 = c^2\), right triangle.
• If \(a^2 + b^2 > c^2\), acute triangle.
• If \(a^2 + b^2 < c^2\), obtuse triangle.

Here, \(a = 7\), \(b = 15\), \(c = 17\) (since 17 is the longest side).

Step2: Calculate \(a^2 + b^2\) and \(c^2\)

Calculate \(a^2\): \(7^2 = 49\)
Calculate \(b^2\): \(15^2 = 225\)
Sum: \(49 + 225 = 274\)

Calculate \(c^2\): \(17^2 = 289\)

Step3: Compare the two results

Since \(274 < 289\) (i.e., \(a^2 + b^2 < c^2\)), the triangle is obtuse.

Answer:

obtuse