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. What type of triangle is being depicted from the measurements?

Answer 1

Shape of Triangular sail is Obtuse Angled Triangle.

Explanation:

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!

Given: Length of sides of triangular sail = 7 ft , 15 ft , 7 ft

To find: Shape of Sail .i.e., shape of triangle

We use a result which states that

if a , b , c are sides of triangle where c is greater then a & b.

now, if c² < a² + b² then triangle is Acute angled

if c² = a² + b² then triangle is Right angled

if c² > a² + b² then triangle is Obtuse angled

here a = 7 , b = 7 & c = 15

c² = 15² = 225

a² + b² = 7² + 7² = 49 + 49 = 98

since, c² > a² + b²

⇒ Triangle must be Obtuse Angled.

Therefore, Shape of Triangular sail is Obtuse Angled Triangle.