** Lets learn about the Acute Angled triangle (AAT), Right Angle Triangle (RAT) and Obtuse Angled Triangle in this Post **

**Acute Angled Triangle**

When all the Angles of a Triangle are less than 90°, we call such a triangle as an AAT .

For Example – **∆ ABC is an AAT as all the three angles i.e, ∠BAC, ∠ACB and ∠ABC are less than 90° (Acute Angle).**

**Right Angled Triangle – RAT**

When one angle of a triangle is 90° and the other two angles are acute ( less than 90°) then we call such a triangle as a RAT.

For Example – In **∆ ABC ∠BAC is 90° ( right angle ) and ∠ACB and ∠ABC are less than 90° ( acute angle ).**

**Obtuse angled triangle**

If one angle of a triangle is obtuse ( greater than 90°) and other two are acute ( less than 90°), we call such a triangle as Obtuse angled triangle.

For Example – **∆ABC is an Obtuse Angled triangle as ∠BAC is 110° (obtuse angle) and ∠ACB and ∠ABC are acute angle (less than 90°). **

**EXAMPLE 1**

If the measure of the angle of the triangle are 56 ˚ , 49 ˚ and 75 ˚, then the triangle is —- Triangle ?

**EXPLANATION**

Here,

56 ˚ < 90 ˚

49 ˚ < 90 ˚

75 ˚ < 90 ˚

Since, all the three angles of triangle are **less than 90˚, h**ence, the triangle is An **AAT. **

**EXAMPLE 2**

If the measure of the angle of the triangle are 90 ˚ , 54 ˚ and 36 ˚, then the triangle is?

**EXPLANATION**

Here,

**90 ˚ = 90 ˚ **54 ˚ < 90 ˚

36 ˚ < 90 ˚

Since, one angle is** 90˚** and the other two angles are acute angle (less than 90˚, hence, the triangle is a **Right Angled Triangle.**

**EXAMPLE 3**

If the measure of the angle of the triangle are 93 ˚ , 55 ˚ and 32 ˚, then the triangle is?

**EXPLANATION**

Here,

**93 ˚ > 90 ˚ **55 ˚ < 90 ˚

32 ˚ < 90 ˚

Since, one angle of a triangle is** obtuse **( **greater than 90˚** ) and other two are acute angles (less than 90˚)

Hence, the triangle is an **Obtuse Angled Triangle **