The angles of elevation of the top of a rock from the top and foot of a 100 m high tower are respectively 30° and 45°. Find the height of the rock.
Answers
height of the rock = 236.6 m
Step-by-step explanation:
Height of tower = 100 m
Height of Rock (from foot of tower) = h m
height of rock from top of tower = h - 100 m
Tan 45 = Height of rock from foot of tower / Horizontal Distance between rock & tower
=> 1 = h/Horizontal Distance between rock & tower
=> Horizontal Distance between rock & tower = h
Tan 30 = Height of rock from top of tower / Horizontal Distance between rock & tower
=> 1/√3 = (h-100)/h
=> h = h√3 - 100√3
=> h√3 - h = 100√3
=> h = 100√3 /( √3 - 1)
=> h = 100√3 ( √3 + 1) /(3 - 1)
=> h = 50√3 ( √3 + 1)
=> h = 150 + 50√3
=> h = 150 + 86.6
=> h = 236.6 m
height of the rock = 236.6 m
Learn more:
Length of the shadow of a person is x when the angle of elevation is ...
https://brainly.in/question/2107666
The angle of elevation of top of a minor and angle of depression of ...
https://brainly.in/question/13899214
{ 17}[/tex]At distances of 18m and 2m the angles of elevation of a
https://brainly.in/question/14684087