Vertical tower angles of depression of two cars in the same straight line with the base of the tower attention are found to be 45 degree and 60 degree is the cars are 100 m apart on the same side of the tower find the height of the tower
Answers
Dear Friend!
Question: →
→ From the Vertical tower angles of depression of two cars in the same straight line with the base of the tower attention are found to be 45° and 60° is the cars are 100 m apart on the same side of the tower find the height of the tower?→
Method of Solution: →
→ Given Statement: Two cars in the same straight line with the base of the tower attention are found to be 45° and 60°° with each other!✔
→ Now, Let to be Distance between car and the vertical tower is 'x'✔
Considering on Question Statement!✔
In ∆ABC, Tan 60° = BC/AB
→ • √3=BC/AB
→ √3=h/x
→ h=√3x -------(1)✔
Again, In Triangle ∆DBC, Tan 45°=BC/DB
Tan 45°=BC/DB
→ 1= h/x+ 100
→ h=(x+100) -------(2)✔
From Equation (1) and (2), we get!
→ √3x -x = 100
→x(√3-1)=100
→ x(1.732-1)=100
→x(0.732)=100
→ x = 100/0.732✔
•°• Value of x be (136.61)metres ✔✔
Therefore, Required Height of tower (√3×136.61) =236.60metres→
Hence, Required height of the tower is (236.60metres )
→
√3=BC/AB
=> √3=h/x
=> h=√3x --(1)
Tan 45°=BC/DB
1= h/x+ 100
h=(x+100) -(2)
From Equation (1) and (2),
√3x -x = 100
=x(√3-1)=100
= x(1.732-1)=100
=x(0.732)=100
=x = 100/0.732
Value of x 136.61metres
Height =√3×136.61 =236.60 metres
Hence, height of the tower is (236.61)