# 007 Components of a force parallel and perpendicular to the incline

**Problem 007**

A block is resting on an incline of slope 5:12 as shown in Fig. P-007. It is subjected to a force F = 500 N on a slope of 3:4. Determine the components of F parallel and perpendicular to the incline.

**Solution 007**

$\theta = \alpha + \beta$

$\theta = \arctan (3/4) + \arctan (5/12)$

$\theta = 59.49^\circ$

$F_x = 500 \cos \theta = 500 \cos 59.49^\circ$

$F_x = 253.85 \, \text{ kN}$ *answer*

$F_y = -500 \sin \theta = -500 \sin 59.49^\circ$

$F_y = -430.77 \, \text{ kN}$ *answer*