Question 418919: A water tower 30 m tall is located at the top of a hill. From a distance of D = 145 m down the hill, it is observed that the angle formed between the top and base of the tower is 8°. Find the angle of inclination of the hill. Round your answer to the nearest tenth degree.
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! A water tower 30 m tall is located at the top of a hill. From a distance of D = 145 m down the hill, it is observed that the angle formed between the top and base of the tower is 8°. Find the angle of inclination of the hill. Round your answer to the nearest tenth degree.
..
Draw a hill sloping down from left to right with an unknown inclination =x
At the top of the hill draw a vertical line which represents the 30 meter tower.
From the top, point A, draw a line to a point which makes a given 8 deg angle
with the surface of the hill. Call this point, B. The bottom of the tower, point C, to point B, along the surface is given to be 145 meters. Extend the vertical line into the hillside to a point, C, from which it is connected to point B at right angles. We now have two triangles to work with. First we have an obtuse triangle ABC with given sides of 30 and 145 meters and an angle of 8 deg. The second is a right triangle, CBD,with sides CD and CB,and an angle of inclination, x. Both triangles have side BD in common.
..
calculations:
let x=angle of inclination of hillside
sin 8 deg/30=sin A/145
sin A=145 Sin 8 deg/30=.673
angle A=42.3 deg
obtuse angle = 180-42.3-8=128.7 deg
angle CDB 180-128.7=50.3 deg
angle of inclination, x=90-50.3=39.7 Deg
ans:
Angle of inclination of hill=39.7 degrees.
|
|
|
