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=

$\frac{ {b}^{2} + {c}^{2} - {a}^{2} }{2bc} \\ = \frac{ {45}^{2} + {27}^{2} - {36}^{2} }{2 \times 45 \times 27} \\ = \frac{3}{5} = 0.6$

or, A= cos^-1(0.6)=53.13°

similarly, cosB=

$\frac{ {a}^{2} + {c}^{2} - {b}^{2} }{2ac} \\ = \frac{ {36}^{2} + {27}^{2} - {45}^{2} }{2 \times 36 \times 27} \\ = 0$

or, B= cos^-1(0)=90°

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