Question

On the packaging for a triangular sail, the edge measurements for the sail are listed as 7ft x 15ft x 17ft without unfurling the sail, you want to determine if the sail forms a right triangle, an acute triangle or an obtuse triangle

Answer 1

The law of cosines can be helpful here. The largest angle (C) will be opposite the longest side (c). That law tells us ...

... c² = a² + b² -2ab·cos(C)

Then

... cos(C) = (a² +b² -c²)/(2ab)

We don't actually need the angle. We only need to know the sign of the cosine.

... cos(C) = (7² +15² -17²)/(2·7·15) = -15/210 . . . . negative sign, so C > 90°

The sail has the shape of an obtuse triangle.

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A triangle solver app on your calculator, phone, tablet, or computer can give you the result easily.

Answer 2

The law of cosines can be helpful here. The largest angle (C) will be opposite the longest side (c). That law tells us ...

... c² = a² + b² -2ab·cos(C)

Then

... cos(C) = (a² +b² -c²)/(2ab)

We don't actually need the angle. We only need to know the sign of the cosine.

... cos(C) = (7² +15² -17²)/(2·7·15) = -15/210 . . . . negative sign, so C > 90°

The sail has the shape of an obtuse triangle.

_____

A triangle solver app on your calculator, phone, tablet, or computer can give you the result easily.

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