on the packaging for a triangular sail, the edge measurements for the sail are listed as 7 ft × 15 ft × 17…

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.

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.

Answer

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}<c^{2}), it is an obtuse triangle.

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}<c^{2})), the triangle is obtuse.

Answer:

obtuse