## Question

What is the resultant force when two forces 10n and 20n are inclined at angle 60 to each other?

### Answer:

**Final outcome: The final answer to the above question is 26 Newtons**

**Explantion**

**Data:** Important information from the question

The first force, F_{1} = 10N

The second force, F_{2} = 20N

The angle between the forces, θ = 60^{0}

**Unrevealed Values:**

Resultant, R = ?

**Formula:** Equation that will help us solve the problem

We will apply the formula below to solve the problem

R^{2} = F_{1}^{2}+ F_{2}^{2} – 2 F_{1} F_{2} Cos ( 180^{0} – θ )

#### Solution

We will insert our data into the formula to solve the problem

R^{2} = F_{1}^{2}+ F_{2}^{2} – 2 F_{1} F_{2} Cos ( 180^{0} – θ ) = 10^{2}+ 20^{2} – 2 (10) (20) Cos ( 180^{0} – 60^{0} )

Thus, our resultant will become

R^{2} = 100 + 400 – 400 x ( – 0.5 )

Hence,

R^{2} = 500 + 200 = 700

We will now apply the square root to both sides to obtain

R = √700 = 26.5 N = 26 N

Therefore, the resultant force when two forces 10 Newton and 20 Newton is 26 Newton

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