Acute Angled Triangle | Obtuse Angled Triangle | Right Angled Triangle

Acute Angled triangle – When all the Angles of a Triangle are Acute angles ( less than 90°), we call such a triangle as an Acute angled triangle.

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

Right Angled Triangle – 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 Right angled triangle.

For Example – ∆ ABC is a Right Angled Triangle as ∠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°). 

Acute Angled Triangle, Right Angled Triangle and Obtuse Angled Triangle – Examples

EXAMPLE 1

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

EXPLANATION

Acute Angled Triangle – When all the Angles of a Triangle are Acute angles ( less than 90°), we call such a triangle as an Acute angled triangle.

Right Angled Triangle – 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 Right angled triangle.

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.

here,
56 ˚ < 90 ˚
49 ˚ < 90 ˚
75 ˚ < 90 ˚

Since, all the three angles of triangle are acute angles (less than 90˚)

Hence, the triangle is An Acute Angled Triangle. 

EXAMPLE 2

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

EXPLANATION

Acute Angled Triangle – When all the Angles of a Triangle are Acute angles ( less than 90°), we call such a triangle as an Acute angled triangle.

Right Angled Triangle– 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 Right angled triangle.

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.

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

Acute Angled Triangle – When all the Angles of a Triangle are Acute angles ( less than 90°), we call such a triangle as an Acute angled triangle.

Right Angled Triangle – 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 Right angled triangle.

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.

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