An angle is a space that is shared by two rays that are joined at the same vertex. We can even find different types of angles according to their amplitude. If the amplitude is larger than 90º and less than 180º that tells us that it is an obtuse angle.

An obtuse triangle is defined as an angle that is formed when a ray rotates between 90º and 180º around a point.

Obtuse Angle Triangle Formula

Area of an obtuse angle triangle = ½ *b*h

where b is the base and h is the height of the triangle.

Properties of Obtuse Angled Triangle

  • When an obtuse triangle XYZ has two angles acute and one angle obtuse.
  • Perpendicular bisectors of the three sides XYZ intersect at the circumcenter of the circle.
  • When medians are drawn from X, Y, and Z  and they intersect at the centroid of the triangle.
  • When three sides are given the triangle can be drawn.
  • When three sides are given the area of the triangle can be calculated.

Special Facts about Obtuse Triangle

  • Did you know that an equilateral triangle can never be obtuse? Since an equilateral triangle has equal sides and angles and each angle measures 60° which is acute. Equilateral angles can never be obtuse-angled.
  • A triangle cannot be right-angled and obtuse-angled at the same time. A right-angled triangle has one right angle and the other two angles are acute.

Some Examples of Obtuse Triangle

  • Blades of a ceiling fan
  • Clock showing 8 o’clock
  • Base of a tripod
  • A fully opened cupboard door
  • A coat hanger
  • A clothes stand
  • Steering wheel of the car
  • A book kept open for reading
  • Shower nozzle
  • Flowers arranged in a vase
  • Triangle shaped roofs

Examples of Obtuse Triangle in Everyday Life

Have you ever noticed that you can find obtuse triangles around you? There are quite a few examples.

  • In analog clocks, you can find even more examples of times when obtuse angles are formed by the clock hands, for example, 3:35.
  • When ballerina dancers are able to stretch their legs to an amplitude that is characteristic of an obtuse angle. If they are able to maintain their balance and the amplitude then they can turn to the other side and the angle would still measure the same.
  • When someone eats more than a quarter of a pizza but less than half. The part of the pizza which is missing is an obtuse angle.
  • The angle formed by the excavator’s arm forms an obtuse angle so that it is able to dig into the soil further away than if it were a smaller angle.

Obtuse angles are seen mostly on the house rooftops, as the two roof surfaces slope down from it.  There are some real-world examples of an obtuse angle which include the angle between the screen and the base of an opened laptop, a hockey stick, an accordion hand fan, etc. Whenever the two sides, arms, or surfaces deviate widely then it is observed as an obtuse angle.

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