Discussion Topic

Determining the perimeter of triangle ABC with given sides and angles

Summary:

To determine the perimeter of triangle ABC, you need to sum the lengths of all three sides. If the side lengths are given, simply add them together. If only angles and some sides are provided, you may need to use trigonometric relationships or the law of sines or cosines to find the missing side lengths before calculating the perimeter.

Expert Answers

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Determine the perimeter.Determine the perimeter of triangle ABC if AB=6, B=pi/4, C=pi/6.

For the triangle ABC AB = 6, B=pi/4, C=pi/6.

As the angles of a triangle have a sum of pi. A = 7*pi/12

Use the property sin A/a = sin B/b = sin C/c

c = 6, C = pi/6, B = pi/4 and A = 7*pi/12

=> sin (pi/6)/6 = sin (pi/4)/b = sin (7*pi/12)/a

=> b = 8.485

=> a = 11.59

The perimeter of the triangle is 6 + 8.48 + 11.59 = 26.07

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An illustration of the letter 'A' in a speech bubbles

TrianglesDetermine the perimeter of triangle ABC if AB=6, B=pi/4, C=pi/6.

For the triangle ABC AB = 6, B=pi/4, C=pi/6.

As the angles of a triangle have a sum of pi. A = 7*pi/12

Use the property sin A/a = sin B/b = sin C/c

c = 6, C = pi/6, B = pi/4 and A = 7*pi/12

=> sin (pi/6)/6 = sin (pi/4)/b = sin (7*pi/12)/a

=> b = 8.485

=> a = 11.59

The perimeter of the triangle is 6 + 8.48 + 11.59 = 26.07

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