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.

Answer 1

The triangle is obtuse since the sum of the squares of 2 sides are greater than the square of the third side. (Converse Pythagorean theorem) Hope this helps!

Answer 2

By applying the converse of the Pythagorean theorem, the general shape of the triangular sail is an obtuse triangle.

• Let the sides of the triangular sail be a, b and c respectively.

Given the following data:

• a = 7 ft

• b = 15 ft

• c = 17 ft

To determine the general shape of the triangle, we would apply the converse of the Pythagorean theorem:

The converse of the Pythagorean theorem states that in a right angle triangle, the square of the third side of a triangle is equal to the sum of its two (2) shorter sides.

Mathematically, the converse of the Pythagorean theorem is given by:

For a right angle triangle:

• $c^2 = a^2 + b^2$

For an obtuse triangle:

• $c^2 > a^2 + b^2$

For an acute triangle:

• $c^2 < a^2 + b^2$

Substituting the given parameters into the formula, we have;

$17^2 = 7^2 + 15^2\\\\289 = 49 + 225\\\\289 = 274\\\\289 > 274$

Therefore, the general shape of the triangular sail is an obtuse triangle.

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