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 |
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°.
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:
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.
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 = \(\sqrt\) 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.
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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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.
Example 2: Find the area of an acute scalene triangle whose base is 10 units and height is 12 units. Solution: The formula for a scalene acute triangle area is (1/2) × b × h square units. By substituting the values of base and height in this formula, we get (1/2) × 10 × 12 square units. ⇒ Area = 5 × 12 ⇒ Area = 60 square units Therefore, the area of the given triangle is 60 square units.
Example 3: What will be the length of the third side of an acute scalene triangle if its perimeter is 68 inches and the lengths of the other two sides are 20 inches and 27 inches respectively? Solution: The formula of acute scalene triangle perimeter is a+b+c units, where a, b, and c are the sides of the triangle. Here, two of the sides are given as 20 inches and 27 inches. By using the perimeter formula, we can find the length of the third side. a + b + c = 68 20 + 27 + c = 68 47 + c = 68 c = 68 - 47 c = 21 inches Therefore, the length of the third side of the triangle is 21 inches.
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