Verified Answer :

81^2 = 18 ^2 + 80^
6561 = 324 + 6400
6561 = 6724
It is not a right angle, since 18^2 + 80^2 does not equal 81^2.
So,
Using The law of cosines:
The largest angle C is opposite to the side c.
Therefore, 
c^2 = a^2 + b^2 -2ab cosC 
Here,
 c^2 < (a^2 + b^2)
 cosC must be positive which makes C an acute angle. 

A triangle that has side lengths of 18 cm, 80 cm, and 81 cm is an acute triangle.

Acute Triangle

Acute triangle is a type of triangle in which all the three internal angles of the triangle are acute, that is, they measure less than 90.

Therefore, let's use the side to find the angles.

cosine law

80² = 18² + 81² - 2 × 18 × 81 cos A

6400 = 324 + 6561 -

6400 = 6885 - 2916 cos A

6400 - 6885 = -2916 cos A

-485 = -2916 cos A

A = cos⁻¹ 0.16632373113

A = 80.4272375636

A = 80.4°

using sine law

80 / sin 80.4 = 18 / sin B

cross multiply

80 sin B = 17.7479286673

sin B = 17.7479286673 / 80

B = sin⁻¹ 0.22184910834

B = 12.8147776823

B = 12.8°

C = 180 - 80.4 - 12.8 = 86.8°

Therefore, the triangle is an acute triangle because all its angles are less than 90 degrees.

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