Obtuse Scalene Triangle
An obtuse scalene triangle is a special type of triangle that shows the properties of both the obtuse triangle and scalene triangle. All three sides and angles are different in measurements. And, one of the three angles of an obtuse scalene triangle lies between 90° and 180°.
| 1. | Obtuse Scalene Triangle Definition |
| 2. | Properties of Obtuse Scalene Triangle |
| 3. | Obtuse Scalene Triangle Formulas |
| 4. | FAQs on Obtuse Scalene Triangle |
Obtuse Scalene Triangle Definition
In geometry, an obtuse scalene triangle can be defined as a triangle whose one of the angles measures greater than 90 degrees but less than 180 degrees and the other two angles are less than 90 degrees. All three sides and angles are different in measurement. Look at an obtuse scalene triangle given below whose one of the angles is greater than 90° and the other two angles are acute angles (less than 90 degrees).
Properties of Obtuse Scalene Triangle
An obtuse scalene triangle displays the properties of both the obtuse triangle and scalene triangle. An obtuse triangle is one whose one of the angles is obtuse (lies between 90 degrees and 180 degrees) and a scalene triangle is one whose all three sides and angles are different in measurement. So, the obtuse scalene triangle properties are listed below:
- It has two acute angles and one obtuse angle.
- All the sides and angles are different in measure.
- The sum of all three interior angles is 180°.
Obtuse Scalene Triangle Formulas
The formula of scalene obtuse triangle helps us to find the area and perimeter of the triangle quickly. Let us learn about these formulas in detail.
Obtuse Scalene Triangle Area
The area of an obtuse scalene triangle is given as Area = (1/2) × b × h square units. Here, "b" denotes the base, and "h" denotes the height of the triangle.
Note: If all the sides of the scalene obtuse triangle are given, then the area of an obtuse scalene triangle can be easily calculated using Heron's formula given below.
Area of an obtuse scalene triangle using heron's formula = \(\sqrt{S(S-a)(S-b)(S-c)}\) square units. Here, S denotes the semi perimeter which can be calculated as S = (a + b + c)/2, and a, b, and c are the sides of the given triangle.
Perimeter of Obtuse Scalene Triangle
The perimeter of an obtuse scalene triangle is defined as the sum of the three sides and it is given as, P = (a + b + c) units. Here, a, b, and c are the sides of the triangle. It gives the total length required to form a scalene obtuse triangle. We use the perimeter to draw or make an obtuse scalene triangle with a rope, thread, pencil, etc.
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Obtuse Scalene Triangle Examples
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Example 1: Find the height, if the area of the given obtuse scalene triangle PQR is 40 square inches and the base is 8 inches.
Solution: The given triangle PQR is an obtuse scalene triangle. We know that area (△PQR) = 40 in2 and base = 8 in. Now, by applying the area formula, we get,
⇒ Area = (1/2 × b × h) square inches
⇒ 40 = 1/2 × 8 × h
⇒ h = (40 × 2)/8
⇒ h = 10 inches
Therefore, the height of the given triangle PQR is 10 inches.
FAQs on Obtuse Scalene Triangle
What is an Obtuse Scalene Triangle?
An obtuse scalene triangle is a type of triangle in which all three sides and angles are of different measurements. Two of its angles are acute and it has one obtuse angle. It has the features of both obtuse triangle and scalene triangle.
What are the Properties of an Obtuse Scalene Triangle?
The properties of an obtuse scalene triangle are listed below:
- Two angles are acute (less than 90 degrees) and one angle is obtuse (greater than 90 degrees but less than 180 degrees).
- Unequal sides.
- Unequal angles.
What Set of Angles can Form an Obtuse Scalene Triangle?
Two unequal acute angles and one obtuse angle can form an obtuse scalene triangle. So, if we have two unequal angles each of them must be less than 90 degrees, 1 angle between 90 and 180 degrees and the sum of all three angles must be 180 degrees, then we can form an obtuse scalene triangle.
Can you have an Obtuse Scalene Triangle?
Yes, it is possible to draw an obtuse scalene triangle. There are three possible types of obtuse triangles that are possible which are scalene obtuse triangle, isosceles obtuse triangle, and equilateral obtuse triangle. In an obtuse scalene triangle, there are three unequal sides and angles.
How to Draw an Obtuse Scalene Triangle?
To draw an obtuse scalene triangle, the first step is to draw a line segment which will be the base of the triangle. Then, construct an obtuse angle on one end of that segment and join it with the other end of the segment. This way we will get an obtuse scalene triangle.
How to Find the Area of an Obtuse Scalene Triangle?
To find the area of an obtuse scalene triangle whose base and height are given, we use the following formula: Area = [(1/2) × base × height] square units.