Question

the line joining the top of the hill to the foot of the hell makes an angle of 30 degree with the horizontal through the foot of the hill then is one Temple at the top of the hill and the guest house half way from the foot of the talk the talk of the temple and of the guest house both make and elevation of 45 degrees at the foot of the hills is the gas is 1 kilometre away from the foot of the hills Around The Hills find the height of the guest house and the temple

Answer 1

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  1k m away from the foot of the hill

To Find :  the heights of the guest  house and the temple

Solution:

Height of Hill = 2d  km

Height of point of Guest house = d   km

Tan 30  = d/1

=> 1/√3  = d/1

=> d = 1/√3

2d = 2√3

Horizontal Distance of  hill = 2 km

a = height of guest house

Tan 45 = (d + a) /1

=> 1  = ( 1/√3 + a)/1

=> 1 =1/√3 + a

=> a =  ( 1  - 1/√3)

=>  a = ( √3 - 1)/√3

=> a = 0.4226 km

b = height of temple

Tan 45 = (2d + b) /2

=> 1 = (2/√3 +  b) /2

=> 2 = 2/√3 + b

=> b =  2 ( 1  - 1/√3)

=> b =2 ( √3 - 1)/√3

=> b = 0.8453 km

height of guest house =0.4226 km  =   422.6 m

height of temple =0.8453 km  =      845.3 m

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Answer 2

Answer:

the line joining the top of the hill to the foot of the hell makes an angle of 30 degree with the horizontal through the foot of the hill then is one Temple at the top of the hill and the guest house half way from the foot of the talk the talk of the temple and of the guest house both make and elevation of 45 degrees at the foot of the hills is the gas is 1 kilometre away from the foot of the hills Around The Hills find the height of the guest house and the temple