The line joining the top of a hill to the foot of the hill makes an angle of 30° with the
horizontal through the foot of the hill. There is one temple at the top of the hill and a
guest house half way from the foot to the top. The tops of the temple and of the
guest house both make an elevation of 45° at the foot of the hill. If the guest house is
100 m away from the foot of the hill along the hill, find the heights of the guest
house and the temple. (13=1.732)
Answers
Given : The line joining the top of a hill to the foot of the hill makes an angle of 30° with the horizontal through the foot of the hill. There is one temple at the top of the hill and a guest house half way from the foot to the top. The tops of the temple and of the guest house both make an elevation of 45° at the foot of the hill.
the guest house is 100 m away from the foot of the hill
To Find : the heights of the guest house and the temple
Solution:
Height of Hill = 2d
Height of point of Guest house = d
Tan 30 = d/100
=> 1/√3 = d/100
=> d = 100/√3
2d = 200√3
Horizontal Distance of hill = 200 m
a = height of guest house
Tan 45 = (d + a) /100
=> 1 = ( 100/√3 + a)/100
=> 100 = 100/√3 + a
=> a = 100 ( 1 - 1/√3)
=> a = 100 ( √3 - 1)/√3
=> a = 42.26 m
b = height of temple
Tan 45 = (2d + b) /200
=> 1 = (200/√3 + b) /200
=> 200 = 200/√3 + b
=> b = 200 ( 1 - 1/√3)
=> b =200 ( √3 - 1)/√3
=> b = 84.53 m
height of guest house = 42.26 m
height of temple = 84.53 m
Learn More:
From top of a small hill,the base of a vertical cliff has an angle of ...
https://brainly.in/question/17473853
If the angle of elevation of a cloud from a point h metres above a lake
https://brainly.in/question/6575589