The smallest angle in a 345 −− right-angled triangle is very close to 37°. From the top of a symmetric hill of height 600 m, the angle of depression of a point at its base is 37°. Find the width (diameter) of the hill’s base.
Answers
Given : From the top of a symmetric hill of height 600 m, the angle of depression of a point at its base is 37°
To find : the width (diameter) of the hill’s base.
Solution:
Angle of Depression = Angle of elevation
=> angle of elevation = 37°
Height of hill = 600 m
Radius of hill Base = R
Tan angle of elevation = Height of hill/Radius of Hill Base
=> Tan 37° = 600/R
( using the given fact that The smallest angle in a 3 , 4 , 5 −− right-angled triangle is very close to 37° => Tan 37° = 3/4 )
=> (3/4) = 600/R
=> R = 800
Radius of hill Base = 800 m
width (diameter) of the hill’s base. = 2 * Radius = 2 * 800 = 1600 m
width (diameter) of the hill’s base. = 1600 m
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Given : From the top of a symmetric hill of height 600 m, the angle of depression of a point at its base is 37°
To find : the width (diameter) of the hill’s base.
Solution:
Angle of Depression = Angle of elevation
=> angle of elevation = 37°
Height of hill = 600 m
Radius of hill Base = R
Tan angle of elevation = Height of hill/Radius of Hill Base
=> Tan 37° = 600/R
( using the given fact that The smallest angle in a 3 , 4 , 5 −− right-angled triangle is very close to 37° => Tan 37° = 3/4 )
=> (3/4) = 600/R
=> R = 800
Radius of hill Base = 800 m
width (diameter) of the hill’s base. = 2 * Radius = 2 * 800 = 1600 m
width (diameter) of the hill’s base. = 1600 m