Question

A gutter at the edge of a roof drops 2 inches for every 30 feet of length. The measure of the angle to the nearest tenth of a degree that the gutter makes with the roof is ____ degrees. (Enter only the number.)

Answer 1

1 foot = 12 inches,

so 1 in=1/12 ft,

this means 2 in=2/12=0.1667 ft.

check the picture,

let the black line segment represent 30 ft of the roof, the blue line segment represent the gutter.

let α be the angle formed by the roof and the gutter.

tan α =(opposite side)/(adjacent side)= 0,1667/30=0.00556

then, α=arctan(0.00556)=0.39 (degrees)

the last result is found using a scientific calculator or other software.


Answer: 0.39 (degrees)