Question

if the angles of elevation of a tower from two points at distances a and b where a>b from its foot and in the same straight line from it are 30° and 60° respectively, find the value of √a/b​

Answer 1

Step-by-step explanation:

Given:-

The angles of elevation of a tower from two points at distances a and b where a>b from its foot and in the same straight line from it are 30° and 60° respectively.

To find:-

find the value of √a/b

Solution:-

The angles of elevation of a tower from two points a and b are angle ADB = 60° and

angle ACB = 30°

Let the height of the tower be h units

AB = h units

AD= b units

AC = a units

Now ,

From ∆ADB ,a right angled triangle

Tan θ = Opposite sides/Adjacent side

Tan 60° = AB/BD

=>√3 = h/b

=>h = √3 b units----------(1)

From ∆ACB,a right angled triangle

Tan θ = Opposite sides/Adjacent side

=>Tan 30°= AB/BC

=>1/√3 = h/a

On applying cross multiplication then

=>√3 h = a

=> h = a/√3 units -----(2)

From (1)&(2)

=>√3b = a/√3

=>√3b×√3 = a

=>3b = a

=>3 = a/b

=>√3 = √(a/b)

=>√(a/b)=√3

Answer:-

The value of √(a/b) for the given problem is√3

Used formulae:-

• .Tan A = Opposite sides/Adjacent side
• Tan 30°=1/√3
• Tan 60°=√3