Question

Using the side lengths determine whether the triangle is acute, obtuse or right 36, 45, 27

Answer 1

given sides,

a=36

b=45

c=27

From cosine law,

cosA=

`\frac{ {b}^(2) + {c}^(2) - {a}^(2) }{2bc} \\ = \frac{ {45}^(2) + {27}^(2) - {36}^(2) }{2 * 45 * 27} \\ = (3)/(5) = 0.6`

or, A= cos^-1(0.6)=53.13°

similarly, cosB=

`\frac{ {a}^(2) + {c}^(2) - {b}^(2) }{2ac} \\ = \frac{ {36}^(2) + {27}^(2) - {45}^(2) }{2 * 36 * 27} \\ = 0`

or, B= cos^-1(0)=90°

Since, B=90, the given triangle is right angled triangle.