A Person Standing at a distance of 90 m
from a church observes the angle of
elevation of the top top 45 digree Find
the height of the Church
Answers
Answer:
Answer:
Step-by-step explanation:
We will trigonometric ratios in this question.
Here we have two right angled triangles with a common height.
One has the following properties.
Adjacent angle = 45° and height h
The other one has adjacent angle = 60° and height h.
Let the remaining distance to the base of the tower be x.
The total distance to the base of the tower from the point the man began will be :
(x + 20) cm
At angle of elevation 45° :
Base = (x + 20)cm
h = height
h = (x + 20) / Tan 45°
At angle of elevation 60°:
Base = x cm
h = height
h = xTan 60°
Equating the two we have :
(x + 20)Tan 45 = xTan 60
Tan 45 = 1
Tan 60 = √3
Doing the substitution we have :
x + 20 = x√3
x + 20 = x√3
x + 20 = 1.7321x
1.7321x - x = 20
0.7321x = 20
x = 27.32 m
height = 27.32 + 20 = 47.32 m
= 47.32 m
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