A triangle whose a**ll sides are acute angle** is known as Acute Triangle

**What is Acute Angle?****Angle below 90 degree** measurement is known as acute angle

Hence in acute angle triangle, all the angle measurement is below 90 degrees

**Examples of Acute Triangle**

Given above are the example of acute angle triangle.

Note all the angles of triangle are below 90 degrees

**Types of Acute Angle**

There are three types of acute angle possible:

(a) Scalene Acute Triangle

(b) Isosceles Acute Triangle

(c) Equilateral Acute Triangle

The definition of each angle is self explanatory:**Scalene Acute Triangle**

Acute Triangle in which length of all sides are different are called Scalene Acute Triangle

Here all the angles are also measured differently

**Isosceles Acute Triangle**

It’s an Acute Triangle in which length of two sides are equal

Here two angles are of same measurement

**Equilateral Acute Triangle**

Its an Acute triangle in which length of all sides are equal

All angles measures 60 degrees

Examples of all the triangles are shown in below image

**Acute Angle Properties**

**(01) In the acute triangle, there will be no angle measuring exact or more than 90 degree**

**(02) The circumcenter of acute triangle lies inside the triangle**

**What is Circumcenter?**

Its a center of the circle through which circle can be drawn which will touch all the vertex of triangle

**Example**

Given above is acute triangle ABC and circumcenter O through which circle can be drawn touching all the vertex of the triangle.

**How to locate the circumcenter in acute triangle?**

Circumcenter is a point formed by the intersection of two perpendicular bisectors of triangle

Let us find circumcenter of the below triangle using following steps:

**Step 01**

Take compass rounder and draw perpendicular bisector of side BC

**Step 02**

Similarly draw perpendicular bisector of line AB

**Step 03**

The point where two perpendicular bisector meet is the circumcenter of the triangle.

Label the point as O

**Conclusion**

The circumcenter of acute triangle lies inside the triangle

**(03) Centroid of acute triangle lies inside the triangle**

**What is centroid?**

Centroid is the midpoint of the geometrical figure.

It can be located at the point of intersection of the medians

Let us find the centroid of the given acute triangle HGI using following steps

**Step 01**

Find the midpoint of side GI and draw straight line touching the midpoint and vertex of opposite side

The line MN is the median of side GI

**Step 02**

Similarly draw the median on other two sides

The point O is the intersection of median.

This point is also the centroid of the triangle.

**Conclusion**

In acute triangle, the centroid lies inside the triangle

**(04) Similar to the circumcenter and centroid, other points like orthocenter and incenter also lines inside the triangle**

**Area of Acute Triangle**

There are two formulas for calculation of Area of Acute Triangle.

(a) Formula when height and base length is given

(b) Formula when length of all sides are given

**Area formula when base length & height is given **

Area of triangle = \frac{1}{2} \times \ b\ \times h\

**Area Formula when all sides are given**

Given below is an acute triangle with side length a, b and c

Follow the below steps for area calculation

**Step 01**

Calculation of semi perimeter (S)

S\ =\ \frac{a+b+c}{2}

**Step 02**

Use the below area formula

Area\ =\sqrt{S\ ( S-a)( S-b)( S-c)}

This formula is also known as **Heron’s formula**

Remember both the formulas as it will help to solve different math problems.

**Frequently Asked Questions – Acute Triangle**

**(01) Is the below image is of acute triangle?**

NO!!

Angle B is 96 degree which is not an acute angle.

In acute triangle, all the angles are acute angles

**(02) Can acute triangle has two equal sides?**

Yes

In acute isosceles triangle, two sides are equal to each other and all angles are acute angle

**(03) In acute triangle, can all the angle be equal to each other**

Yes, in equilateral acute triangle, all the angles are equal measuring 60 degree

**(04) In acute triangle, is circumcenter and centroid lie on same location?**

NO!!

These points lie inside the triangle but their location is different