Angle in a triangle

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June 4th 2010, 06:20 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)????
June 4th 2010, 06:28 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 ...

$<br /> a^2 = b^2+c^2 - 2bc\cos{A}<br />$

rearrange ...

$<br /> \cos{A} = \frac{b^2+c^2-a^2}{2bc}<br />$
June 4th 2010, 06:28 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)

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

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