80. A boulder of weight $w$ rests on a hillside that rises at a constant angle $\alpha$ above the horizontal, as shown in Fig. $1.42$. Its weight is a force on the boulder that has direction vertically downward. (a) In terms of $\alpha$ and $w$, what is the component of the weight of the boulder in the direction parallel to the surface of the hill?

 80. A boulder of weight $w$ rests on a hillside that rises at a constant angle $\alpha$ above the horizontal, as shown in Fig. $1.42$. Its weight is a force on the boulder that has direction vertically downward. (a) In terms of $\alpha$ and $w$, what is the component of the weight of the boulder in the direction parallel to the surface of the hill? (b) What is the component of the weight in the direction perpendicular to the surface of the hill? (c) An air conditioner unit is fastened to a roof that slopes upward at an angle of $35.0^{\circ} .$ In order that the unit not slide down the roof, the component of the unit's weight parallel to the roof cannot exceed $550 \mathrm{~N}$. What is the maximum allowed weight of the unit?