Question

please po help me.

A chimney projects 6 feet above the roof. At a point 10 feet 8 inches down the roof from the base of the chimney,the chimney subtends an angle of 17°40' . find the angle at which the roof is inclined to the horizontal.

Answer 1

draw a diagram. extend the chimney downward to where it meets a horizontal line drawn from the point Q 10'8" down the roof. Label
T = top of chimney
B = bottom of chimney
PQ = base of right triangle TPQ.

using the law of sines,
6/sin17°40' = 10'8"/sinT
sinT = 10.666*sin17°40'/6 = 0.5395
T = 32.65°

So, in triangle TBQ, angle B = 129.68°

Thus, the angle of the roof (BQP) is
90-(180-129.68) = 39.68°
Call it 40°