Question

If the sides of a triangle are 13, 7, 8
the greatest angle of the triangle is
(a) π/3
(b) π/2
(c) 2π/3
(d) 3π/2​

Answer 1

2π/3

Step-by-step explanation:

Let the side be

• a = 13
• b = 7
• c = 8

Largest angle would be opposite largest size.

So,

cosA = (b² + c² − a²) / 2bc

cosA = (49 + 64 - 169) / 2×7×8

cosA = -1/2 = cos 120°

A = 120° = 2π/3

Answer 2

Given: The sides of a triangle are 13, 7, 8.

To find: We have to find the greatest angle.

Solution:

The three sides of a triangle are 13, 7, 8.

Let a=13

b=7 and c=8.

Now let the largest angle of the triangle be x and it is opposite to that of the largest side.

The formula of largest angle is-

$\cos(x) = \frac{ {b}^{2} + {c}^{2} - {a}^{2} }{2bc}$

Putting the values of a, b and c in the above equation we get-

$\cos(x) = \frac{ {7}^{2} + {8}^{2} - {13}^{2} }{2 \times 7 \times 8} \\ \cos(x) = \frac{49 + 64 - 169}{14 \times 8} \\ \cos(x) = \frac{-1}{2} \\cosx=cos120°\\cosx=cos(2π/3)\\x=2π/3$

The value of x is 2π/3.

The largest angle of the triangle is 2π/3.

The correct option is c.