How to Find an Angle in a Obtuse Triangle

With any three values of a triangle's three sides and three angles, you can determine an unknown angle.

Triangles are one of the staples of mathematics, and understanding their function is essential to the comprehension of numerous everyday life phenomena. However, before you can use them, you have to understand the six pieces of information in a triangle: the lengths of the three sides, and the size of the three angles. To find an unknown angle, Q, you must possess at least three of these pieces of information. With this information, you can apply the Law of Cosines to solve for the unknown angle.

Instructions

1. Find an unknown angle T when you know the value of the other two angles by subtracting those values from 180, the number of degrees in an ordinary flat triangle.

2. Find an unknown angle Q when you know the length of all three sides of the triangle by this formula:

   angle Q = arccos (( a² + b² -- c² ) / ( 2ab ))

   ...where "c" is the length of the side of the triangle opposite to angle Q.

3. Find an unknown angle Q when you know the length of two sides, a and b, and the angle between them, C, by this formula for the third side of a triangle, c:

   c = sqrt ( a² + b² -- 2ab cos C )

   Then use the lengths of the three sides of the triangle to determine angle Q.

4. Find an unknown angle Q when you know the length of two sides, b and c, and one of the two angles, C, not between them (and not angle Q) by this formula for the third side of a triangle, a:

   a = b cos C ± sqrt ( c² -- b² sin² C )

   Then use the lengths of the three sides of the triangle to determine angle Q.

Tips & Warnings

• You can also use a protractor to measure an unknown angle, if your triangle is a real-world triangle, or if it is a facsimile drawn to scale.

References

• Cut the Knot: The Law of Cosines