Question

two forces 5N and 10N are acting with an inclination of 120 degree between them. what is the angle which their resultant makes with 10N​

Answer 1

Let P be the force of 5 N and Q be the force of 10 N.

By parallelogram law of vector addition, the resultant is,

R2=P2+Q2+2PQcosθ

R2=25+100+100cos120∘

R=53N

Let α be the angle made by R with 10 N

tanα=P+QcosθPsinθ

tanα=5+10cos1205sin120

tanα=31

α=30∘

Answer 2

Given:

two forces 5N and 10N are acting with an inclination of 120 degrees between them.

Find:

what is the angle which their resultant makes with 10N​?

Solution:

Let P be the force of 5 N and Q be the force of 10 N.

By parallelogram law of vector addition, the resultant is,

$R2=P2+Q2+2PQ$  cosθ

$R2=P2+Q2+2PQ$  cosθ

$R2=25+100+100$  cos120∘

$R=53N$

Let α be the angle made by R with 10 N

tanα=P+QcosθPsinθ

tanα=5+10cos1205sin120

tanα=31

α=30∘