A closed 2D figure having three sides of either same or different lengths and three angles of same or different angles are called triangles. A triangle with one obtuse angle i.e; one of the interior angles measure more than 90 degrees and the remaining two acute angles are called an obtuse triangle. In an obtuse triangle, if one of the angles measures more than 90°,then the sum of the remaining two angles must be less than 90°.
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What is an Obtuse Angle?
Since, we are learning about an obtuse-angled triangle, thus we must know what is an obtuse angle?
When we join any two line segments end to end, there are basically three types of angles that can be formed and they are as follows:
- Acute angle
- Right angle
- Obtuse angle
When two line segments are joined in such a way that the angle between them is less than 90 degrees,then the formed angle is acute angle and the resulting triangle formed from this angle is called an acute angle triangle.
A right angle is formed when one line segment is exactly perpendicular to another line segment at the joining points and the angle between them is 90 degrees, the triangle resulting from that angle is called a right angle triangle. Now, when two line segments are joined in such a way that the angle between them is more than 90 degrees, this is called Obtuse angle. When we join the remaining two open ends of the line segments, then it forms an obtuse-angled triangle. And, if you want to know more about the type of angles that form shapes like obtuse triangles you can visit the Cuemath website.
Properties of Obtuse triangle
- An obtuse triangle has two acute angles and the third angle is obtuse.
- The perpendicular bisectors of the three sides of the obtuse triangle intersect at the circumcenter of the circle.
- The medians are drawn from all the 3 vertices of the obtuse triangle intersect at the centroid of the triangle.
- The circumcenter of an obtuse triangle will always lie outside the triangle.
- The angle bisectors of the three angles of the obtuse triangle, intersect at the incenter of the circle. With that incenter of angle bisectors of an obtuse triangle, a circle can be drawn to touch the three sides internally.
- Each of the three medians will split the triangle into two smaller triangles of the same area.
- If we join the midpoints of the three sides, and you get 3 parallelograms of the same area.
Area and Perimeter of Obtuse triangle:
For an obtuse triangle, the formula of area and perimeter is similar to the formula of any other triangle.
Area of the triangle is as given by the following expression:-
Area = 1/2 × b × h
where,b= base of triangle
h=height of triangle
Or,
A=√s(s−a)(s−b)(s−c)sq.units
Where s = (a+b+c)/2 (s= semiperimeter)
a, b and c are the lengths of the sides of the triangle in the above expression.
The perimeter of the triangle is always equal to the sum of all the sides of the triangle.
Hence,
Perimeter = a+b+c
a,b and c are sides of a triangle in the above expression.
you can visit cuemath website for a more detailed description.
Obtuse Triangle Examples in Real Life:
We can find many examples of obtuse triangles in our surroundings. Following are some of the examples:
- Triangle shaped roofs
- Hangars found in cupboards
Some Facts About Obtuse Triangle:
- An equilateral triangle can never be obtuse. Since an equilateral triangle has all of the three sides and angles are equal, thus each angle measures 60°, which is acute. Therefore, an equilateral triangle can never be obtuse-angled.
- A triangle cannot be a right-angled triangle and an obtuse-angled triangle at the same time. Since a right-angled triangle has one right angle and hence the other two angles must be acute. Therefore, an obtuse-angled triangle can never have a right angle and a right angled triangle can never have an obtuse angle.
- The opposite side of the obtuse angle in the triangle is the longest side of the triangle.