Answer to Question #100617 in Trigonometry for gab

Question

maria needs to load cars onto a transport truck. she is plannng to drive up a ramp, onto the truck bed. the truck bed is 1.5m high, and the maximum angle of the slope of the ramp is 35 degrees.
a) how far is the rear of the truck from the point where the ramp touches the ground?
b) how long should the ramp be?

Answer 1

AC = the truck bed;

AB = the length of the ramp;

CB = length of the rear of the truck from the point where the ramp touches the ground.

a) $tan 35^\circ={\cfrac{AC}{CB}}$ ;

$CB ={\cfrac{AC}{tan35^\circ}}={\cfrac {1.5}{0.7}}\approx 2.14 m$ ;

b)

$sin 35^\circ={\cfrac{AC}{AB}}$ ;

$AB ={\cfrac{AC}{sin 35^\circ}}={\cfrac {1.5}{0.5736}}\approx 2.62 m$ .