. A road is going up a hill and makes a 15% angle with the ground. The height of the hill is 25 yd. How long is the road?

We need to use the sine for this.....we know an angle, an opposite side..... and we need to find the hypoteneuse.....

We have....

sin(15) = 25/h    ...where h =  the hypoteneuse = road length

Multiply both sides by h and divide both sides by sin(15)..so we have...

h = 25/sin(15) = (about 96.6 yds)

15/100=tg(alpha)=25/lenght of the road

0.15=25/lenght

lenght=25/0.15

lenght=166.666

15/100=tg(alpha)=25/lenght of the projection of the road on the ground

0.15=25/proj

proj=25/0.15

proj=166.666

lenght=sqrt(proj^2+height^2)=168.524