Acute Scalene Triangle
An acute scalene triangle is a special type of triangle that shows the properties of both acute triangle and scalene triangle. All three sides and angles are different in measurements. And, all three angles of an acute scalene triangle are less than 90°.
| 1. | Acute Scalene Triangle Definition |
| 2. | Properties of Acute Scalene Triangle |
| 3. | Acute Scalene Triangle Formulas |
| 4. | FAQs |
Acute Scalene Triangle Definition
In geometry, an acute scalene triangle can be defined as a triangle whose angles are less than 90 degrees and all three sides and angles are different in measurement. Look at an acute scalene triangle given below whose angles are 65°, 35°, and 80°.
Properties of Acute Scalene Triangle
An acute scalene triangle displays the properties of both acute triangle and scalene triangle. An acute triangle is one whose all angles are acute (less than 90 degrees) and a scalene triangle is one whose all three sides and angles are different in measurement. So, the acute scalene triangle properties are listed below:
- It has three acute angles.
- All the sides and angles are different in measure.
- The sum of all three interior angles is 180°.
Acute Scalene Triangle Formulas
The formula of scalene acute triangle helps us to find the area and perimeter of the triangle quickly. Let us learn about these formulas in detail.
Acute Scalene Triangle Area
The area of an acute 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 acute triangle are given then the area of an acute scalene triangle can be easily calculated using Heron's formula given below.
Area of an acute 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 Acute Scalene Triangle
The perimeter of an acute 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 acute triangle. We use the perimeter to draw or make an acute scalene triangle with a rope, thread, pencil, etc.
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Acute Scalene Triangle Examples
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Example 1: Find the missing angle ∠PRQ in the triangle given below. And identify the type of triangle.
Solution: It is given that ∠RPQ=56° and ∠PQR=74°. We know that according to the angle sum property of triangles, the sum of all three interior angles of any triangle is 180°. So, ∠PQR + ∠PRQ + ∠RPQ = 180°.
⇒ 74° + ∠PRQ + 56° = 180°
⇒ ∠PRQ + 130° = 180°
⇒ ∠PRQ = 50°
Therefore, the missing angle is 50°. Since all three angles of the given acute triangle are different, it is an acute scalene triangle.
FAQs on Acute Scalene Triangle
What is an Acute Scalene Triangle?
An acute scalene triangle is a type of triangle in which all three sides and angles are of different measurements and all three angles are less than 90 degrees. It has the features of both acute triangle and scalene triangle.
What are the Characteristics of an Acute Scalene Triangle?
The characteristics of an acute scalene triangle are listed below:
- All three angles are acute angles (less than 90 degrees).
- Unequal sides.
- Unequal angles.
What Set of Angles can Form an Acute Scalene Triangle?
Three unequal acute angles can form an acute scalene triangle. So, if we have three unequal angles each of them must be less than 90 degrees and the sum of all three angles must be 180 degrees, then we can form an acute scalene triangle.
Is an Acute Scalene Triangle Possible?
Yes, it is possible to draw an acute scalene triangle. There are three possible types of acute triangles that are possible which are scalene acute triangle, isosceles acute triangle, and equilateral acute triangle. In an acute scalene triangle, there are three unequal sides and angles.
How to Draw an Acute Scalene Triangle?
To draw an acute scalene triangle, the first step is to draw a line segment which will be the base of the triangle. Then, construct two acute angles on each end of that segment such that the sum of those should be greater than 90 degrees. Then draw the lines that will pass through those angles and will meet at a point which will be the third vertex of the triangle.
How to Find the Area of an Acute Scalene Triangle?
To find the area of an acute scalene triangle whose base and height are given, we use the following formula: Area = [(1/2) × base × height] square units.