# 009 Force with given component parallel to the incline

**Problem 009**

The body on the 30° incline in Fig. P-009 is acted upon by a force P inclined at 20° with the horizontal. If P is resolved into components parallel and perpendicular to incline and the value of the parallel component is 1800 N, compute the value of the perpendicular component and that of P.

**Solution 009**

$\theta = 20^\circ + 30^\circ$

$\theta = 50^\circ$

**Perpendicular component**

$P_n = 1800 \tan \theta = 1800 \tan 50^\circ$

$P_n = 2145.16 \, \text{ N}$ *answer*

**Value of P**

$P = \dfrac{1800}{\cos \theta} = \dfrac{1800}{\cos 50^\circ}$

$P = 2800.3 \, \text{ N}$ *answer*

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