# Angle in a triangle

• Jun 4th 2010, 07:20 AM
Mukilab
Angle in a triangle
The length of the sides of a triangle are 4.2, 5.3 and 7.6.

Calculate the size of the largest angle of the triangle to 1 dp.

How would I know this without calculating the area using 1/2 a b sin(c)????
• Jun 4th 2010, 07:28 AM
skeeter
Quote:

Originally Posted by Mukilab
The length of the sides of a triangle are 4.2, 5.3 and 7.6.

Calculate the size of the largest angle of the triangle to 1 dp.

How would I know this without calculating the area using 1/2 a b sin(c)????

use the law of cosines ...

$
a^2 = b^2+c^2 - 2bc\cos{A}
$

rearrange ...

$
\cos{A} = \frac{b^2+c^2-a^2}{2bc}
$
• Jun 4th 2010, 07:28 AM
masters
Quote:

Originally Posted by Mukilab
The length of the sides of a triangle are 4.2, 5.3 and 7.6.

Calculate the size of the largest angle of the triangle to 1 dp.

How would I know this without calculating the area using 1/2 a b sin(c)????

Hi Mukilab,

Use the law of cosines. Let C be the largest angle (opposite 7.6)

$c^2=a^2+b^2-2ab \cos C$