Question

31. From the top of a vertical tower, the angles of depression of two cars
the same straight line with the base of the tower, at an instant are
to be 45° and 60°. If the cars are 100 m apart and are on the same side
ICBSE
the tower, find the height of the tower.
biran electric fault on a pole of height​

Answer 1

Question:

From the top of a vertical tower, the angles of depression of two cars in a straight line with the base of the tower at an instant are to be 45 ° and 60°. If the cars are 100 m apart and are on the same side of the tower find the height of the tower.

Answer:

$\bigstar{\bold{Height\:of\:tower\approx 237\:m}}$

Explanation:

$\Large{\underline{\underline{\bf{Given:}}}}$

• Angles of depression of two cars are 45° and 60°
• Distance between two cars = CD = 100 m

$\Large{\underline{\underline{\bf{To\:Find:}}}}$

• Height of the tower = AB

$\Large{\underline{\underline{\bf{Solution:}}}}$

→Let AB = h, BD =  x

→ Consider Δ ABD

  tan 45 = AB/BD

  tan 45 = h/x

   1 = h/x

   h = x ------equation 1

→ Consider Δ ABC

   tan 60 = h/x - 100

   √3 = h/x - 100

   √3 ( x - 100 ) = h

→ Substitute the value of x from equation 1

  √3 ( h - 100 ) = h

   h√3 - 100 √3 = h

   h√3 - h = 100√3

   h ( √3 - 1 ) = 100√3

   h = 100√3/ ( √3 - 1 )

→ Substituting the value of √3 as 1.73 we get,

  h = 100 × 1.73 (1.73 - 1)

  h = 173/ 0 .73

  h ≈ 237 m

$\boxed{\bold{Height\:of\:tower\approx 237\:m}}$

$\Large{\underline{\underline{\bf{Notes:}}}}$

$sin\:A=\dfrac{opposite}{hypotenuse}$

$cos\:A=\dfrac{adjacent}{hypotenuse}$

$tan\:A=\dfrac{opposite}{adjacent}$